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Full text of "Monthly Notices of the Royal Astronomical Society"

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i/r6 :7 - -^^' 




IZlABD-SUNfORD-JVNIOR-VIJlVEBSnY 



/ 



// 






; 



MONTHLY NOTICES 



OF THE 



ROYAL ASTRONOMICAL SOCIETY, 



CONTAINING 



PAPERS, 



ABSTKACTS OF PAPERS, 



AND 



KEPORTS OF. THE PROCEEDINGS 



OF 



THE SOCIETY, 



FROM NOVEMBER 1876 TO XOrEMBEli 1877. 



VOL. XXXVII. 



. 1 I t t 



|)nnttD bn 

SPOTTISWOODE & CO., NEW-STREET SQUARE, LONDON. 

1877. 



t I \ 



273662 



• " • 



.• -•- 



• • • 



• • • • 



• . • 



• • • 
* -* - 



•• • • 

a • * 



,•• 



LIST OF THE FELLOWS 



• •' 



.N.- 



OF THB 



ROYAILi ASTRONOMICAL SOCIETY, 



JUNE 1877. 



An a^torisk (*) prefiioed to a name indicates that the Member has oomponnded for his Annual ContrI> 
bfations ; a dagier (t) IniH oa t i e a « Non-rerident Member ; and a doable dagger (%) a Member of the 
late Mmthfpmatloal Society ; aU of whom are exempted from the Annual ContribatiOD. 

Stould amp trrvrt or omissions be/ouiui in this List, U is rtqufskd that notice th ^eqf bt given to thf Secretaries. 



PATRONESS. 

Her Majesty QUEEN VICTORIA. 



FELLOWS. 



Date of Election. 
i833> Feb. 8 

1870, Apr. 8 
1876, Jan. 14 
i860, Jane 8 
1870, Apr. 8 



1845, Nov. 14 



1869, Mar. 12 
1828, May 9 



1865, J<^* '3 



* Bicbard Abbatt, Esq., Marlborough Eimie, Burgess Hill^ 

Sussex, 
Rev. Richard Abbay, WadJiam College, Oxford, 

♦ Prof. Cleveland Ahhc, Armg Weath^ Bureau,Washingfon,V,S. A, 
Francis Abbott,E8q., Observatory , Ilobart Torcn, Tasmania, 
Capt. Wm. de Wiversley Abney, R.E. F.R.S., 3 St,Alban's Road, 

South Kensington, S, W, 

♦ John Couch Adams, Esq., M.A. LL.D. F.R.S., Lowndean 

Professor of Astronomy in the University of 
Cambridge, Vice-President, Observatory, 
Cambridge, 
Major-Gen. Thomas Addison, C.B., Hill House, MeUon,- Suffolk, 

* Sir Gbobgb Biddell Aiby, K.C.B. M.A. LL.D. D.C.L. F.R.S., &c., 

Astronomer- Royal, Vice-President, Eoyal 
Observatory, Oreenmch, S,E. 
John Derby Allcrof t, Esq., 108 La ncaster Oate, Hyde Pa rh, W, 



qp'^b ASTRONOMICAL SOCIETY. (June 1877) 






Date of Eleotioif. fA 
1876, Marr JO •} * 



■ • • 



• • * 



i8j^i^. 10 
-. i86>>i9ov. 8 

^54, Mar. 10 
. '1875, I^e<5' 10 

1875, -^Pr. 9 

1853, Dec 9 
1875, Jan. 8 



1873, Apr. 9 
1 875) J&Q* 8 
1877, June 8 

1877, Jail' 12 
1875, Mar. 12 



1849, 
1856, 

1877, 

1874, 
1850, 
1876. 
1870, 
1869, 



Dec. 14 
Feb. 8 
Jan. 12 
Dec. 14 
May 8 
Dec. 13 
Jan. 14 
Nov. II 
Mar. 12 



1835, Mar. 13 
1863, Nov. 13 
1863, May 8 

1857, Jan. 9 

1827, May II 
1870, Apr. 8 
1877, May II 
1832, May II 



William James Allsnp, Esq., 5 Eattcamhe nZ2a«, Blaehkeathy 

S.E. 
George Spedding Almond, Esq., Daisy Sill, D&wihury, 
Thomas Mitchell Almond, Esq., i$a St, Helen's Place, E,C. 
Joseph Snpino Ancona, Esq., 8 John Street, Adelphi, W,C, 
Senor Augosto T. Arcimis, Cadiz, 
Carl • Armbmster, Esq., F.C.S. F.Z.S., The Limes, 

Mortlahe, S.W. 
Commander E. D. Ashe, B.N., Quebec, 
A. Duncan Austin, Esq., IweeroargiU, New Zealand, 



* T. W. Backhouse, Esq., West Hendon House, Sunder* 

land, 
G. S. Baden-Powell, Esq., i Hyde JParh Oate Southj 

S,W. 
Major-Gen. John Baillie, 25 Hamilton Terrace, St, John's Wood, 

N,W. 
Baillie, Esq., 10 Bolton Place, CarUsle, 
Ball, Esq., LL.D. F.B.S., Andrews Professor of 
Astronomy in the University of Dublin, and 
Royal Astronomer of Ireland, Observatory, 
Dunsink Co, Dublin, 
Barber, Esq., B.A., The Old HaU,Spotidon, Derby. 
Barclay, Esq., Kilmarnook, 
Barclay, Esq., C.E., Adelaide, South Australia, 



Robert John 
♦ R. Stawell 



John T. 
Andrew 
Henrv Verc 



* Joseph Gnmey Barclay, Esq., Observatory, Leyton^ Essex. 

Barnacle, Esq., The Vicarage, Knutrford, Cheshire. 
Bameby, Esq., Morton House, Worcester. 
Bameby, Esq., Saltma;rsh Castle, Herefordshire. 
Barrow, Esq., 3 Phillimore Gardens, W, 
Barton, Esq., H,M,S, Conway, Roch Ferry, 

Liverpool. 
Barton, Esq. 
Rev. J. Chadwick Bates, M.A., Castletan Vioarage,near Manchester, 

Baume, Esq., Bourne Lodge, Canterbury JRoad, 

East Brixton, SW, 
Baxendell, Esq., Crescent Bead, Cheetham Hill, 
Manchester. 
t Admiral H. W. Bayfield. 

Bayne, Esq., Brockhill, Broad dyst, Exeter. 
William Morris Beaufort, Esq., F.R.G.S., Athenofum CM, SW, 

* Edward B. Beaumont, Esq., F.R.S.y 33 Norland Square, 

Netting mil^ W. 



H.G. 

Thomas 

William 

♦ Francis 
Charles 

♦ George 
Rev. J. 
Celestin 

♦ Joseph 

t Admin 

♦ W. Thirlwall 



FELLOWS OF THE SOCIETT. (Jane i 770 



Date of EleotioiL 

1861, Feb. 8 
1866, Not. 9 

1862, Apr. II 

1S73, F^* 14 
1872, Dec. 13 

1865, Jan. 13 

1866, Not. 9 

1854, Feb, 10 

1825, June 10 

i869) Jan. 8 
1868, Jan. 10 

i870iNov. II 
1859^ Jan. 14 

iS54» Hay 13 
i869kJui.8 
1861, Jan. II 
1840, Jan. 10 
1861, Feb. 8 

1859, June 10 

1845, Apr. 1 1 
1867, May 10 
i87i,Nov. 10 
1867, Feb. 8 
1849, Dec. 14 

1864, Apr. 8 
1871, June 9 
1866, Feb. 9 

1853, May 13 
1877, Jnne 8 
1873, Nov. 14 
i860, Dec 14 

1855, Peb. 9 



♦ Joseph 

*■ Sir Edmund 



Carl 
J. A. 
Bev. E. Lyon 

* Bev. Frank 

• W.H. 



• Cspt. A. C. 
O. Parker 

Charles 

* Wm. Badcliff 

George 



Beck, Esq., 31 QfmhiU, E,C, 
Beckett, Bart., LL.D. Q.C., 33 Queem Anne 
Street^ W. 
Capt. James F. Beckett, B.K., Za^trittonj Silver BUl^ St, 

Leenards-oH-Sea, 
Behrens, Esq., Dwrhan^ Natal, 
Benmon,Esq., Carpus ChrUti CoUege^ Cambridge, 
Berthon, M.A., Bonuey^ Hants, 
Besant, M.A., ^eey Vtea/rage^ Boitony Lincoln' 

ihire, 
Besant, Esq., M.A. F.B.S., St, John'i College^ 
Ckmbridge, 
Adm. C. B. Drinkwater Bethone, B.N. C.B. 4 Queemherry Place, 

8, W,, and Baf&wTy MarHnchy N,B, 
Bigg- Wither, India, 
Bidder, Esq., Q.C., 6 Cedart' Boadj Clapham 

Common, S, W, 
Bird, Esq., Oramimar School, Bradford, 
Birt, Esq., Sdmkenhwy, Pahnereton Bead, 

Buokhurtt Hill, 
Bishop, Esq., Tivtckenham, & W, 
Bev. Bobt. Hugh Blair, M.A., St, Martin'Sf Worcester, 
Henry Oeorge Bohn, Esq., Henrietta Street, Covent Garden, W, C, 
Major-Oen. John T. Boilean, B.E. F.R.S., z^Ladhroke Square, W, 
Joseph Bonomi, Esq., Sir John Soane^e Micteum, Lincoln's 

Inn Fields, W.C, 

♦ Bev, James Booth, LL.D. F.R.S., Vicarage, Stone, nr. Agios- 

burg, Bucks. 

♦ William Wakeling Boreham, Esq., Haverhill, Suffolk. 
James Whatman Bosanquet, Esq., Claysmore, Enfield, 

B. H. M. Bosanquet, Esq., St, John's College, Oxford, 

♦ Edward E. Bowen, Esq., Sclwol, Harrow, 

Bev. Robert S. Bower, M.A., 19 Park Village West, Albany 

Street, N,W, 
Bowman, Esq., Halifax, 
Brett, Esq., 38 Harley Street, W, 
Brewin, Esq., 2 Copthall Chambers, Throgmcrton 

Street, RC, 
Brewin, Esq., Ide, Exeter, 
Brewin, Esq., 14 St, Nicholas Street, Leicester, 
Bridson, Esq., Bridge House^ BoUon-le- Moors, 

♦ Sir Chas. Tilstone Bright, Kt., 1 1 Delahay Street, Westminster, 

SW, 

♦ Frederic Brodie, Esq., Molseg Oore, Uckfield, Sussex. 



Frederick H. 

John 

Arthur 

Robert 
Thomas D. 
Joseph 



Dfttaof eotion. 

868, Feb. 14 

864, Jan. 8 
865» Apr. 12 
851, Jan. 10 

87s, May 14 

865, Mar. 10 

869, May 14 
860^ May II 
874, Nov. 13 

874»Nov. 13 

874, Nov. 13 

874, May 8 

873, Nov. 14 

871, May 12 
85s, Feb. 9 



877, June 8 
875»Apr. 9 



ROYAL ASTRONOMICAL SOCIETY. (June 1877) 



Charles Henry Brooks, Esq., Simduras. 
Alfred Brothers, Esq., FuUhaWy WilmiloWy Manohuter, 

* Capt. A. Barton Brown, R.A., Ceylan, 
Isaac Brown, Esq., Flounder's Institute^ Achwarthj 

near Pontefraot, 
Capt. Charles Orde Browne, Jkncnhaniy 8h4Hrter$' JERU, Woolmeh, 
John Browning, Esq., ill itfin^rt^, KC.f and 63 

Strand, W.C, 
Dr. Franz F. E. Brunnow, 45 Zeimenttratsef Basel, Switzerland, 
James Buckingham, Esq., The Cedars, East Dulwieh,&E. 

T. H. Budd, Esq., 10 Chilttorth Street, Weethowme 

Thrraoe, W, 
Bumham, Esq., 52 Vtneennes Avenue, Chieago^ 

U.SA, 
Bums, Esq., Coitle Wemyss, Wem/yss Bay, 

Greenock. 
Burton, Esq., Bathmael Bectory, LoughUntUmn, 

Co, Dublin, 
Bush, Esq., The Observatory, Alexandra Bark, 

Nottingham. 
Bushell, Esq. Hinderton, Nesten, Cheshire. 
Harry Wilmot Buxton, Esq., Sydney Street, Fulham Bead, 

iSf.Tr. 



877, June 8 James 



♦ 8.W. 

♦ John 
C. E. 

Thomas W. 
Reginald 



871, Apr. 14 
877, Mar. 9 
867, Feb. 8 

873, Jan. 10 

873, Feb. 14 

849, Jan. 12 
840, June 12 
860, June 8 

1857, July 10 



(George Calver, Esq., Bill Bouse, Wu^ord, CheUnrford. 

Col. Archib, C.C. Campbell, BUfthsivood, near Bet^rew; and 2 

Seamore Place, Curzon Street, W. 

Campbell, Esq., J.P. F.R.G.S.» Arhley Bouse 
Barnet, N, 

Campbell, R.E., India, 

Capron, Esq., Chuildewn, Cfuildford, Surrey, 

Carpenter, Esq., Chester Villa, South Street, 
Oreenfcich, S,E, 

Carpmael, Esq., Streatham Bill, Brixton Bill, 
S.W. 

Carpmael, Esq., Ibmdale, Woodside Road, 
Sutton, Surrey, 

Carrington, Esq. 

Carter, Esq., 61 Cornhill, E,C, 

Casella, Esq., 147 Bolbom Bars, E.C, ; and 
The Lawns, South Grove, Bighgate, 

Caylet, Esq., M.A. LL.D. F.E.S., Sadlerian 
Professor of Pure Mathematics, ViCB- 
Pbbsident, Editor of the Society^s Publica- 
tions, Garden Bouse, Cambridge, 



Capt. W. M. 
J. Rand 
James 

♦ Charles 

♦ Ernest 

G. W. 

John 
Louis P. 

♦ Arthur 



FELLOWS OF THE SOCIETY. (June 1877) 



Dftte of Blfletioa. 



1836, Apr. 8 


Rev. James 


1864, Feb. 13 


Geo. F. 


1859, Nov. II 


♦ Capt. WiUiam 


1872, Jan. 12 


Chintamanny 


1854. Jan- 13 


* James Robert 


1871, Mar. 13 


♦ W. H. Mahony 


1858, July 9 


* Edwin 


1874, Xov. 13 


Latimer 


1873, Dec 12 


W. Kingdon 


i860, Apr. 13 


* Robert Bellamy 


1869, Jan. 8 


Edward 


1874, Jan. 9 


J. Irwin 


1862, Feb. 14 


Hon. J. A. 


1854, Mar. 10 


* Hon. Sir James 


1859, Feb. II 


J. F. 


1862, Mar. 14 


John J. 


1875, Feb. 12 


W. Hammond 


1853, June 10 


Everard Home 


1875, Nov. 12 


♦ John Brise 


185 1, Feb. 14 


Edward John 


1876, Jan. 14 


Rev. Henry 


1869, Nov. 12 


Major Wm. Her 


1876, Jane 9 


Andrew Ainslie 


1S69, May 14 


Thomas 


1864, Feb. 12 


Alfred 


1872, Feb. 9 


Ck>l. E. H. 


184$, June 13 


t Joseph Thomas 



Challis, M.A. F.R.S., Plomian Professor of 
Astronomy in the University of Cambridge, 
2 Trwnpin^iton Street, OtwiMdge, 

Chambers, Esq., Northfteld, Etuthoume, Suuem, 

Chimmo, R.N., Wettdomne, Weymouth, 

Raganootha Chary, Observatory, Madrat. 

Christie, Esq., F.R.S., Arundel House, South 
Norwood Parh, S»E. 

Christie, Esq., M.A., Boyal Observatory, Oreen- 
nneh,&E.; and 12 Boyal Parade, Blachheath^ 
SE. 

Clark, Esq. 

Clark, Esq., 6 Wegtmingter Cha/nibers, Victoria 
Street, SW. 

Clifford, Esq., M.A. F.R.S., Professor of Applied 
Mathematics, University College, Chwer 
Street, W.C, 

Clifton, Esq., M.A. F.R.S., Professor of Experi- 
mental Philosophy in the University of 
Oxford, Portland Lodge, Parh Town, Oxford. 

Clodd, Esq., Bosemaunt, Oarleton Boad, Ttt/nell 
Parh, N, 

Coates, Esq., Southend, Headingley, Leeds, 

Cockbom, Belize, Honduras. 

Cookie, M.A. F.R.S., Chief Justice of Queens- 
land, Brisbane, Australia. 

Cole, Esq., Westfield, Sutton, Surrey. 

Cole, Esq., 24 IHnsbury Circus, E. C. 

Cole, Esq., M.A., India ; and Oreat Plumstead, 
Norwich. 

Coleman, Esq., 71 Brecknoch Boad, Camden 
New Town, JV. 

Colgrove, Esq., Grammar Scliool, Lovghborough. 

CoUingwood, Esq., Lilbtirn To7ver, Almvick, 
Northumberland. 

Collins, EUerton Priory, near Wheldrahe, Yorh. 
Major Wm. Henry Collins, R.E., Brompton Barracks, Chatham, 

Common, Esq., 37 Eaton Bise, Ealing. 

Cooke, Esq., Yorh. 

Cooper, Esq., 29 Clarence Boad, Lower Clapton, 
E. 

QoopeT,Marhree Observatory, Collooney, Ireland. 

Cooper, Esq., 113 Grosvenor Boad, Highbury 
New Parh, N. 



Date of Election. 

1875, Jan. ^ 

1874, J<^* 9 
1871, Apr. 14 
1869, Dec. 10 

1876, Nov. 10 

1862, Feb. 14 
1871, Jan. 13 
1867, Dec 13 

1867, Nov. 8 
1874, Feb. 13 

1863, Feb. 13 

1868, Feb. 14 

1868, Nov. 13 
1863, Jan. 9 
1862, May 9 
1874, Mar. 13 
1848, Apr. 14 
1867, Jnne 14 

1869, May 14 

1858, Har. 12 



187I9 June 9 
1861, June 14 
1855, Mar. 9 
1871, Dec. 8 

1869, Mar. 12 

1875, May 14 

1865, Nov. 10 
1845, J^u^e 13 

1 85 1, Mar. 14 
1877, Jnno 8 

1870, May 13 

1866, Mar. 9 



BOYAL ASTBONOMICAL SOCIETY. (Jmxe 1877) 



W. R. 



♦ Dr. Ralph 
Charles 
Charles J. 

♦ J. Owen 
Arthur 

♦ Samuel 
William 
Samuel 
George 



Cooper, Esq., M.RJl.S., 7 Trinity Terrace^ 
VentnoTf lile qf Wight, 

Copeland, Observatory^ Dun Echt, Aberdeen. 

Coppock, Esq., 38 Arthur JRoad, HoUoway^ N. 

Corbett, Esq. Imber Courts Thames IHtton. 

Corrie, Esq., B.A., Redcctf Putfiey Pa/rh Lane. 

Cottam, Esq., i WhitehaU Place, S.W, 

Cottam, Esq., Higher Bravghton, Manchester. 

Cotterell, Esq., 17 Park Street, WalsalL 

Coortauld, Esq., 76 Lancaster Oate, W. 

Creaser, Esq., MeUha/m, near Huddersfield. 
Rev. Sam. Francis Creswell, D.D. F.R.G.S., Principal of the High 

School, Dublin. 
George Stickland Criswick, Esq., Royal Observatory, Oreenmeh, 

8.E. 

* Edward Crofton, Esq., 45 West Cromwell Road, W. 

* Henry M. E. Crofton, Esq., Inchinappa, Co. Wiokhw, 

* Rev. John Edw. Cross, M.A., Appleby Vicarage, Brigg. 
Richard Cross, Esq., Stafford College, Forest Bill, 8.E. 

* William Assheton Cross, Esq., Bed Scar, near Preston, Lancashire. 

* Edward Crossley, Esq., ffalifax. 

Rev. Robert Crowe, M.A., Woodhouse Vicarage, BudderS' 

field. 
Vice-Adm. Arthur Gumming, C.B., Spring Orove, Bishopstoke$ 

Hants. 



* Rev. Reginald F. 

♦ John Henry 

* John Benjamin 
Duncan 

♦ Rev. Robert P. 

* P. L. H. 

Alfred 
i Charles Orchard 

♦ Warren 

William Fredk. 

Edward 
Henry 



Dale, M.A., i Dean's Yard, Westminster, S. W. 

Dallmeyer, Esq., 19 Bloomsbury Street, W.C. 

Dancer, Esq., Manchester, 

Darroch, Esq., 5 Beaufort Gardens, S, W. 

Davies, M.A., Hatherop, Fairford, Gloucester- 
shire , 

Davis, Esq., Nautical Almafiac Office, 3 Verulam 
Buildings f Oray^s Inn^ W.C. 

Dawson, Esq., The Cedars, ChisTvick, W. 

Dayman, Esq., M.A., Merrie Mead, Milbrook, 
Southampton. 

De La Rue, Esq., M.A. D.C.L. F.R.S., 73 Portland 
Place, W. 

Denning, Esq., TyndaU House, Ashley Down, 
Bristol. 

Dent, Esq., 12 Hyde Park Gardens, W. 

Dodgson, Esq., M.D., Derwent House, Cocker^ 
mouth. 



FBLL0W8 OF THB SOCIBTT. (June 1877.) 



1875, Uar. 12 

1841, May 14 

1868, Jan. 10 
1871, Jan. 13 



1857, Jnly 10 

1875, ^^'^^ 12 
1845, ^^^* 14 

1851, June 13 

1876, Mar. 10 

1877, Jan. 12 

1820, June 9 

1842, Apr. 8 

1871, Feb. 10 
1859, July 8 



1855, Feb. 9 
1864, Dec. 9 
1872, Feb. 9 

1855, Mar. 9 

1864, May 13 

1872, Feb. 9 
1863, Feb. 13 
1858, Mar. 12 

1856, Dec 12 
1875, Mar. 12 
1874, ^V' xo 
1877, Mar. 9 
i8$8, Mar. 12 



Arthur M, W. 
* Solomon Moses 

Colonel A. W. 
Joseph 

Bev. W. H. 



John 
♦ EDwnr 



* Richard 
John William 
Bev. Daniel 

t Bev. James C. 

James 8. 

T. Gwyn Empy 
Robert L. J. 



Henry 8. 

* WiUiam 

* Isaac 

* Wentworth 

Albert 

* J. Kennedy 

* William 

* Rev. Charles 
Capt. F. J. 0. 

* H. Savile W. 
Mortimer 
WiUiam 
R.W. 



Downing, Esq., B.A., Royal Observatory OreeH' 

Drach, Esq., 23 Upper Bamthury Street^ Thorn" 

hiU Boad, N. 
Drayson, B.A., India, 
Drew, Esq., MJL LL.D. F.G.8. F.R.8.L. 

F.R^His.S., 6 Bewnukire Buildingty Wey- 

mouth. 
Drew, M.A., Professor of Mathematics at King's 

College, London, Sowley Homey Warwich 

Bead, W, 
Dreyer, Esq., M.A., Observatory^ Parsonstonm, 

Ireland, 
DUNKIK, Esq., F.R.8., VICE-PRESIDENT, Boyal 

Observatary^. Oreenfeich^ 8,E, ; and Kenwyn, 

Kidbrooke Park Boad, Blackheath, 8,1!, 
Dunkin, Esq., 15 Boyal Plaeey Oreenwiehy 8,E, 
Dorrad, Esq., 12 lAneoln Street^ Leicester, 
Dutton, Sandbaohy Cheshire, 

Ebden, M.A., Cheat 8tukeley Vicarage^ Bunt- 

imgdon, 
EifEe, Esq., M.R.I.A., The Laurels, Txewsley, 

West Drayton, 
Elger, Esq., 8t, Mary, Bedford, 
Ellery, Esq., F.R.S., Superintendent of the 

Astronomical Observatory, Melbourne, Vic 

toria, 
Ellis, Esq., I Ihir Park, near Exeter, 
Ellis, Esq., Boyal Observatory, Oreenmich, S.E. 
Engelson, Esq. 
Erck, Esq., LL.D., Sherrington, Bray, Co. 

IVtcklow, 
Escott, Esq., Boyal Hospital School, Oreenwich, 

S.E, 
Esdaile, Esq., Saint Bill, East Orinstead, 
Esson, Esq., M.A. F.R.S., Merton College, Oxford, 
Evans, M.A., Solihull Beetory, Birmingham, 
Evans, R.N. C.B. F.R.S., Admiralty, S,W, 
Evans, Esq., Wimbledon Park House, Surrey, 
Evans, Esq., 97 West Street, Olasgon, 
Evans, Esq., M.R.C.S., Llanerchymedd, Anglesey, 
Eve, Esq., M.D., Tyrwhitt House, Upper Lewis- 
ham Bead, New Cross, S,E, * 



8 



ROYAL ASTRONOMICAL SOCIETY. (June 1877.) 



Dftte of Kleotion. 


• 


1872, June 14 


Rev. William 


1850, Feb. 8 


♦ Richard 


1858, Dec. 10 


Rev. A. S. 


1849, Mar. 9 


♦ Vincent 


1876, Mar. 10 


Rev. Joseph 


1866, Feb. 9 


Arthur 


1853, J^uie 10 


Thomas 


1873, Nov. 14 


♦ W.H. 


1864, May 13 


H.P. 


1861, Feb. 8 


Rev. Edward 


1866, June 8 


* Henry Allason 


1849, May II 


Isaac 


1873, Jan. 10 


♦ Professor George 


1859, Dec 9 


Rev. P. A. 


185 1, June 13 


♦ WiUiam 


1864, Jan. 8 


* Rev. Alexander 


1871, Nov. 10 


J.H. 


1838, May II 


♦ General Edw. 


1838, Apr. 13 


William 


1870, Jan. 14 


♦ William 


1836, Nov. II 


♦ Rev. Thomas 


1870, May 13 


♦ Charles Henry 


1872, Dec. 13 


♦ E. 


1857, Jan. 9 


William B. 


1874, 1)ec II 


H.J. 


1867, Dec 13 


♦ David 


1857, Mar. 13 


W, S. 


1841, May 14 


* James 


1871, Apr. 14 


♦ J. W. L. 


1874, May 8 


♦ Joseph 



Falconer, M.A., Buthey, Wtttford, Serti, 
Farley, Esq., 62 Wrotham Boad^ Chmden Ttmn^ 

N.W. 
Farrar, D.D., CoUsge, Durham, 
Fasel, Esq., 8 Bne de la Gore, Morget, Switzer* 

land. 
Ferguson, The Mantes Old Hill, Dudley. 
Finch, Esq., Christ Church Bead, Baupell Park, 

S.W. 
Finch, Esq., M.D., Westville, Mary Churchy 

Ibrquay. 
Finlay, Esq., Beyal Ohtervatoryy Cape ijf Good 

Hope. 
Finlayson, Esq., 16 Tarh Street 9 Dover, 
Firmstone, MJL., Wineheeter. 
Fletcher, Esq., Croft HtU, Whitehaven. 
Fletcher, Esq., M.P. F.R.S., Ibm Bank, Qtrlisle. 
Forbes, Ander$on*t Uhivenity, Glasgow. 
Fothergill, 5 Boyal Terrace, Southend. 
-Francis, Esq., Ph.D. F.L.S., Sec, Manor Souse, 

Biehmond, S. W. 
Freeman, M.A., St. John^s College, Cambridge. 
Freeman, Esq., Stratford House, Stra^ord, E. 
Frome, R.E., EnseU, Surrey. 
Frost, Esq., Wentworth Lodge, Upper Tulse 

Hill, S W. 

Gamett, Esq., Bashall Lodge, CUtheroe. 

Gaskin, M.A. F.R.S., 7 PitviUe Lamn, Chelten- 
ham. 

Gatty, Esq., Felbridge Park, East Grinstead. 

Gay, Esq., Calmitta, and Orchaston, Devizes. 

Gibbs, Esq., Medina Villa, Knight's Hill, Lower 
Norwood. 

Gibson, Esq., Junior St. James's Club, St. Jama's 
Street, S.W. 

Gill, jun., Esq., 48 Skene Terrace, Aberdeen. 

Gillett, Esq., Harefield, Bittern, Southampton. 

Glaisher, Esq., F.R.S., i Dartmouth Place, 
Blackheath, S.E. 

Glaisheb, Esq., M.A. F.R.S., Secbbtabt, 
Trinity College, Cambridge. 

Gledhill, Esq., Bermerside Observatory, Skireoat, 
Halifax. 



FELLOWS OF THE 80CISTT. (June 1877.) 



Ml of: 
i8d4,Dea 9 
1872, Jan. 12 

1847, Jan. 8 

1874, Jan. 9 
1860^ June 8 

1858^ Not. 12 
i85o» June 14 

I&I7, Mar. 12 

1851, KoT. 14 

1875, P®^« i^ 
1868, Jan. 10 
1868, Dec. II 
1870^ Nov. II 

1873, Not. 14 

1855, Jan. 13 
1820^ Apr. 14 

1875, ^^v* 12 
1877, Feb. 9 
1854, Jan. 13 
1839, Dec. IS 

1870, Feb. II 

1876, Jan. 14 

1845, P^^« 14 

1843, ^^^' 10 
i86o» Mar. 9 
1873, May 9 

1864, Feb. 12 



BeT. N. 8. 
William 

* Bev. H. Albert 

BeT. Dr. 0. R. 
Sandford 

♦ Cyril 0. 

♦ Robert 

Peter 

* WiUiam 
Nathaniels. 
Robert Fhillipe 
Rev. Charles 
Howard 

Lient. Q. F. 



Godfrey, 8t, BaHkohmew'9 Panonage^ Smthsett. 
Godward, Bsq., 22 Wray CresoetUt Upper 

Goodwin, -M.A. F.C.P.S., lamboume Beetory^ 

Gordon, 3 Norlamd Plaee^ Netting HiU, W. 
Gorton, Bsq., Pc^mkam Houeey Pembwry Boady 

Clapton, J3, 
Graham, Esq., 9 Cleveland Row, St. Jame8% 8, W, 
Giant, Esq., LL.D. F.R.8., Regius Professor of 

Astronomy, Ohiervatory, Qlaegow, 
Gray, Esq., 20 8t. Atiyuitine^i Bead, Camden 

Sjuare^NW. 
Gray, Esq., 6hray*i Qmrtf Mintter Yard, York, 
Green, Esq., 3 drvui Bead, St, John*i Wood, N. W, 
Greg, Esq., CoU'i Park, Buntingford. 
Gribble, BritUh Embauy, Constantinople, 
Gmbb, Esq., 17 LHmter Squa/re, Bathminet, 

DubUn. 
(hiyon,7tillV«ili^«,i2^AflN<milParrMib,l>i»&Kfi. 



George Hamilton, Esq., Queen^i CoUege, JAvefpook 

t The Tezy Ber. H. P. Hamilton, M.A. F.R.S. &c. Dean of Salisbury, 

Deanery, SaUeiury, 
Major-Gen. J. C. Hannyngton, 2 St, 6hmkHn*i ViUoi, Honor Oak, 

SB. 
Gtoorge Francis Hardy, Esq., Botkbury House, Stroud Green, 

I^mhiry Park, N. 

* Bev. Bobert Harley, F.B.S., Burton Bank, MiU HtU, Middle- 

»ew. 
General Sir H.D. Harness, C.B. B.E., Worting, Basingstoke, 

Hants, 
Wm. Augustus Harris, Esq., Phtmley, Bovey Tracy, Devonshire, 

* Augustas S. Harrison, Esq., M.A., Principal of the Moir 

College, Allahabad, India, 
John Hartnup, Esq., Liverpool Observatory, Bidston, 

Birkenhead, 

* Rev. John Moore Heath, M.A., MiUand House, Liphook, Hants, 

* Richard Ford Heath, Esq., EUmbeth House, Oaford, 
William Henry Hennah, Esq., Park House, 24 Pa/rkhurst Bead, 

Camden Boad, N, 
J, B, N, Hennessey, Esq., M.A. F.R.S., Deputy Superin- 

tendent Great Trigonometrical Survey, India, 
and Athenaum CM, & W, 



BOYAL ASTRONOMIOAL SOCIBTY.-* (June 1877O 



Date of BleoUon. 
867, Mar. 8 

872, Feb, 9 
877, Jan. 13 

832, Nov. 8 

873, Feb. 14 
844, Dec. 13 



849, Dec. 14 
866, Jane 8 

868, June 12 
841, Deo. 10 
833* Jan- II 

865, Mar. 10 
849, Dec 14 
873, Dec. 12 
861, Mar. 8 
854, Apr. 12 

866, Jan. 12 
866, Apr. 13 

866, May 11 
861, Feb. 8 



872, June 14 
871, Jan. 13 
876, Feb. II 



840, Mar. 13 
869, Jan. 8 



* Professor Alex. 

* Major John 
Samuel 

* Sir Rowland 
Harris 

* John Russell 



John 

* Thomas Archer 

Henry William 
Rev. Peter 

♦ Charles 

Rev. Robert E. 

* Thomas 

* Joseph 

Rev. Frederick 

♦ William 

♦ Frederick R. 
(George 

Samuel 



* Richard 



H. W. 
Rev. J. 0. 
Rev. William 



♦ Henry W. 
Howel 



Stewart Herschel, College of Phjfii^kil Seienoe^ 

NewoastUf'OH' Tgne, 
Herschel, F.R.S., India. 
Heywood, Esq., 171 Stanhope Street^ Hampitead 

Ready N.W. 
Hill, K.C.B. D.C.L. F.R.S., Hampitead, N.W. 
Hills, Esq., Stamford Bill, N, 
Hind, Esq., F.R.S., Superintendent of the 

Nautical Almanac, Cambridge Park, Twick- 
enham, 
Hippisley, Esq., F.R.S., Stan Eoitan, near Bath, 
Hirst, Esq., Ph.D. F.R.S. Rogal Nacal CoUege, 

Cheenwieh, S,E, 
HoUis, Esq., Keele, Neweattle, Staffordihire, 
Holmes, D.D., Cframmar School, Plymouth, 
Hood, Esq., F.R.S., 10 Leingter Gfardens, Hyde 

Park, W, 
Hooppell, M.A. LL.D., Byen Oreen Rectory, 

WiUington, Co, Durham, 
Hopkirk, Esq., Eltham Lodge, Vietoria Road, 

Duhmch Wood Park, 
Hough, Esq., Head Master of the Orammar 

School, Burnley, Lancashire, 
Hewlett, M.A., Eoit TiHed Rectory, AUon^ 

Sdnti, 
HuGGiNS, Esq., D.O.L.LL.D. F.R.S.,Pbbsidiskt, 

Upper TuUe IRU, S.W. 
Hughes, Esq., Borrofcgtowncu, N,B, 
Hunt, Esq., Hopefield, AUeyn Park, West Bui- 

wich. 
Hunter, Esq., 9 Lower Saokville Street, BuhUn, 



Inwards, Esq., Ida Lodge, Barbome, Bir- 
mingham. 



Jackson, Esq., 15 Limes Terrace, Lewisham,8,B, 
Jackson, M.A., 13 Manor Terrace, Backncy, B, 
Jackson, M.A. F.S.A., 7 Park Place, St, 6files* 

Road East, Oxford; andP(9fi Wartha, Weston- 

super-Ma^e, 
Jeans, Esq., Langstone, near Hdvant, 
Jeffreys, Esq., 5 Brick Court, ^empU, E^C. 



PBLL0W8 OF THE SOCIETY. (June 1877.) 



II 



Date of Seoliofi. 

1874, Jiine 12 
1861, May 10 

1863, May 8 
1874, ^^7 8 
1876, Jan. 14 

1872, Mar. 8 
1852, Jan. 9 
1861, Har. 8 
1865, Feb. 10 

1869, Feb. 12 
1865, Feb. 10 

1865, ^^7 12 

1867, May 10 
1867, June 14 

1872, Jan. 12 

1864, Jan. 8 

i86o» KoT. 9 
1859, May 13 

1869, Jan. 8 

1873, ^^^* 14 

i860y Nov. 9 



C.H. 
Edwaid Daniel 

• Henry 
Richazd 
Richard Coward 

• Bev. 8. J. 
William 
Colonel H. 0. 
B.^ilkin8 

James B. 
Thomas 

♦ W. B. 

♦ John 
Charles 



Johns, Esq., Wiiiton Bouses Winchester, 
Johnson, Esq., 9 Wllminfjtan Square, W,C, 
Johnson, Esq., 39 Orutched Fria/rty E.C. 
Johnson, Esq., 28 TrinAty CoUege, Dublin, 
Johnson, Esq., Higher BeHngton Sail, Birhen- 

head, 
Johnson, M.A., Upton HeUons Rectory, Creditan, 
Johnson, Esq., North Bar, Banbury, 
Johnstone, Bengal Army, India, 
Jones, Esq., 53 Cowley Road, North BriasUm, 

8.W, 
Jones, Esq., Nt^ation School, Aberdeen, 
Jones, Esq., F.O.S., i Brumwich Villas, Shooters* 

BilL 
Jones, Esq., Bigswear Bouse, near CoUford, 

Gloucestershire, 
Joynson, Esq., Waterloo, near Liverpool, 
Judd, Esq., Foundation School, Zeman Street, E, 



1867, Apr. '2 


William 


1870, Apr. 8 


♦ Carlton John 


1873, June 13 


S. J. 


1875, «^^^6 1 1 


John Locke 


1874, May 8 


W.J. 


1869, May 14 


W. Locke 



1S39, June 14 
18691 May 14 



William Bath Kemshead, Esq., Hanover ViUa, Tkurlow Ftirh 

Road, Bulmich, 

* D. J. Eennelly, Esq., 3 Clarence Terrace, Regent^s 

Barh,N,W, 
Bev. Henry Cooper Key, M.A., Rectory, Stretton, Hereford, 
Samuel Kinns, Esq., Ph.D., The CoUege, Highbury New 

Pa/rh,N. 
Capt. James Knight, 6 South Kinning Place, Glasgow. 
E. Ball Enobel, Esq., Vicarage Cottage, St, James* Street, 

WaUhamstow, 

* QeoTge Knott., Esq., LL.B., Cuchfield, Sussex, 



Ladd, Esq., Beah Street, Regent Street, W, 
Lambert, Esq., M.A., Royal Ntwdl CoUege, 

Cheenmoh, S,E, 
Lambert, Esq., Auchland, New Zealand, 
Lancaster, Esq., Oakleigh House, Southend-on- 

Sea, 
Lancaster, Esq., F.C.S. F.G.S. F.R.M.S., Heath- 

field Road, Birmingham. 
Lancaster, Esq., Beavfort House, Cazenove 

Road, Upper Clapton, N, 
Lassell, Esq., LL»D. F.R.S., &c, Ray Lodge, 

Maidenhead, 
Laughton, Esq., Royal Naval College, Oreen- 

Toich, S,E, 



William 



J. Knox 



13 

Dtte of Blectton. 

1873, J^^' l^ 
1868, Jan. 10 
i876»Feb. 11 



1869, Feb. 13 

1856, June 13 

1876, Nov. 10 
1855, Feb. 9 

1849. Apr. 13 

1871, Mar. 30 
1873, Apr. 13 

1873, Feb. 14 

1873, Pe^* 14 
1871, Jan. 13 

1877, Jan. 13 
1863, Mar. 14 

1874, Nov. 14 
1867, Jan. II 

1876, June 9 

1857, Jan. 9 
1848, Jan. .14 

1850, Apr. 13 
1873, Feb. 9 
1861, May 10 
1863, Feb. 14 



ROYAL ASTRONOMICAL 80CIBTY. (June 1877O 



♦ Edwin 
Robert J. 

* Rev. Edmund 



1873, Jan. 10 

1865, Mar. 10 
1838, Nov. 14 
1877, Mar. 9 



♦ John 
Thomas 
Capt. Joseph 
William 
Wm. Ganow 

F. W. 

H. C. 

♦ W.J. 
A. F. 

♦ Lord 

* Louis Stromeyer 
Joseph Norman 

* Edmund Giles 
Benjamin 

* James 

♦ Capt. A. S. H. 
Ed. J. 

Rev. Charles 
D. Lindsay 
Rev. R. C. 

* William Thynne 



W.J. 

* Thomas 

* Sir Thomas 
Frank 



Lawrenoe, Esq., 6 Lanauter Oatdf Hyde Pwrk^ W. 
Lecky, Esq., 3 Lorton I^frraoe, Netting JRU, W, 
Ledger, MJL, Professor of Astronomy in 

Gresham College, Ihufard BeeUry^ Cam' 

hridgeMre, 
Lee, Esq., 8t, Peter' » Chamhen, QfrnkiU, JB,C. 
Lee, Esq., OUervatory^ KUmamoek, 
Leeman, Mercantile Marine Qfiees, Aberdeen. 
Lethbridge, Esq., United Ufweertity CM, 8, W. 
Lettsom, Esq., 3 TkMrlom Place, Lamer. Nerwoodt 

8.E. 
Levander, Esq., 7 Chaleot Crescent, Megent^i 
' Pa/rh Road, N.W, 
Levander, Esq., 30 North VWae, Camden BqyuMre, 

NW. 
Lewis, Esq., Britxtk Mueewn, W.C. 
Lindemann, Esq., Old Charlton, 8,B, 
L1ND8AT, M.P., Foreign Sborbtabt, 47 Br^h 

Street, W. 
Little, Esq., B.A. M.D. Shanghai; and 18 

Parh Street, Qrowoenor Square, W, 
Lockyer, Esq., F.R.S., 16 Penywem Bead, 

South Kemington, SW. 
Loder, Esq., The JRghBeeehes, OramUg, Sueaem. 
Loewy, Esq., 6 SRUdrep Oreeeent, Camden 

Boad,NW: 
Love, Esq., Talbot Ledge, BiehertonBoad, Upper 

HoUowa/g, N 
howe, Hig^ld Houee Obtervatorg, Nottingham. 
Lowe, Esq., F.R.S., Hig^ldffouie Obeervatorg, 

Nottingham, 
Lowndes, M.A., BartweU, near Aylesbnrg, Buehi. 
Lowson, Esq., 164 Kennington Bead, &E. 
Lumsden, M.A., Botemount Lodge, Maidenhead, 
Lynn, Esq., B.A., Bogal Observatorg, Chreen" 

wich,8.E. 



Maodonnell, Esq., 336 C^eorge Street, Sgdneg,N S, 

Walei, 
Mackerith, Esq., Eeclet, Manchester 
Madear, F.R.S., Cape of Qood Hope, 
McClean, Esq., 33 Qreat Qearge Street, West- 
mineter ; and FerncUge^ Tunbridge WelU. 



FELLOWS OF THE SOCIETY. (June 1877) 



13 



Date <tf Etoctioo. 

iSdSyJan. 10 

iS73t Mar. 14 
1S69, June 11 

1865, Feb 10 
1836^ Mar. II 
1840^ Jan. 10 
1845, Jan. 10 

187I9 May 12 
1855, Mar. 9 

1866^ Not. 9 
1872, Jan. 13 

|873f FeK 14 

1875, J^UL 8 

i854t Feb. 10 
1863, Apr. II 
1861, Feb. 8 

1866, Mar. 9 

1869, Nov. 13 
i875» Peb* 12 

i86i» Hay 10 

1877, Mar. 9 

1870, Mar. II 
1863, Jan. 9 
1859, Mar. II 

1865, Feb. 10 

1876, Jan. 14 



1874, Jane 12 
1874, Apr. 10 

1862, May 9 
187 1, Dec 8 
i867» Feb. 8 



James ^'Dowell, Esq., 44 Trumpington Street, Cam- 

bridge, 
* John M^Landsboroogb, Esq., Bnufford, TerkiMre, 

Wm. Worthington Magee, Esq., University College^ Gower Street, 

W.C. 
Magnire, Esq., 6 Wellington Place, Norwich. 
Main, M.A. F.R.S., BadeUffe Ohtercatory^Ojeford. 



* Joseph 
Rer. Bobert 



Rev. Thomas J. Main, M.A., 55 JBeltize Park Gardens, N, W, 



♦ G. 

Henry 
Bobert James 

George 
Frederick J. 

Alexander 

Charles H. 

♦ Arthurs. 

♦ Nicholas 
Samuel 

♦ John 



Man, Esq., care of Frederick W. Dyer, Esq., 1 1 

0t. PuUeney Street, Golden Square. 
Mann, Esq., Cleckheaton, vid Normanton, 
Mann, Esq., M.D., 5 Eingsdanm ViUas^ Wands- 

fcorth Common, S. W. 
Manners, Esq., Zansdonma JRoad, Croydon. 
Marriott^ Esq., Glenwood, Lordship Lane, Dul- 

i^9ieh^ iSL£^. 
Marsden, Esq., M.D., 65 Lincoln's Inn Fields, 

W.C 
Marten, Esq., Combe Lodge, Charlton Jlead, 

Blackheath, S.E. 
Martin, Esq. 
Martindale, Esq. 

Mason, Esq., Sickle Mill, ShoUer JRU, Edslemere. 
Matheson,E8q., 142 West George Street, Glasgow. 
Bev. Alphonso Matthey, 72 Warwiok Gardens, Kensington, W, 
E. W. Maunder, Esq., Boyal Observatory, Greenmch^ 

S.E. 
Bobert Charles May, Esq., 6 6heat George Street, Westminster, 

8.W. 
Meldola, Esq., 21 John Street, Bedford Bow, W. C. 
Meldrum, Esq., F.R.S., Observatory, Mauritius. 
MelhuisbjEsq., 12 York Place,Portmam. Square, W. 
Mellor, Esq., Ths Woodlands, Whitefield, fufar 

Mancheeter. 
Merrifield, Esq., Gascoigne Place, Plymouth 
Messum, Esq.,R.N. F.R.G.S., Controller of H.M. 

Packet Services, Bedford ViUa, Sydenham 

Bead, Croydon, 
Michell, Esq., Tli^ Fort, Newquay, Cornwall. 
Miller, Esq., M.A., Boyal Naval College, Green- 
wich, S.jS. 
Samuel Henry Miller, Esq., 2 Belle Viie Parh, Lowestoft, 

Monk, Mingter Yard, York. 
Morgan, Esq., Sprifigfield House, Bishopsbrigqs, 

near Glasgow, 



B. 

Charles 
Arthur James 

♦ J.J. 

♦ John 
J. Young 



♦ W. Edwards 
B. Kalley 



Dr. E. G. 
* John 



14 

Date of Election. 
1875, Jan. S 

1874, Dec. II 

1851, June 13 

1864, Jan. 8 
iSsSfFeb. II 

1863, Jan. 9 

1875, ^^^ 10 

1873, Feb. H 

1864, May 13 

1875, ^e<^ 10 
1877, Apr. 13 
1862, May 9 

1874, ^^7 8 

1874, Nov. 13 

1875, ^eb. 12 
18549 Jane 9 
1858, July 9 
1855, Jnne 8 
18549 Jane 9 
i86i|Apr. 12 

1871, Jan. 13 



1853, Jan. 14 
1851, Jane 13 
i867»Jan. 11 

1845, Jane 13 
1874, «^*i^ 9 

1867, Jan. II 
1853, Mar. II 

1868, Feb. 14 
1866, Nov. 9 

1877, Jan. 12 



BOYAL ASTRONOMICAL SOCIETY. (Jane 1877) 



G. Staley 
J. Fletcher 

♦ Henry 

J.W. 
Rev. L Vale 

* Richard 



Mosse, Esq., 16 Stanford Road, Ketuinfftim ; and 

Scientifio CM, Savils Bow, W. 
Moulton, Esq., M.A., 74 (huhm Oardmu^ South 

Kentinfltony S.W. 
Mugridge, Esq., Dagmar T^rraee, Prince qf 

WoMiBoad^ Qotport, 
Mnlcaster, Esq., 37 WooUvieh Oommony SK 
Mnmmeiy, 5 St, John*i Terraoe, Buchhunt BxU^ 
Monday, Esq., care of Meurt, BUdreth Jf" Oo^ 

41 NoffoVk Street, W.C. 



Lieat. C. B. Neate, B.N., care qf Meur%, Woodhead 4" OO'i 44 

Charing Cross, 
Edmond Nelson, Esq., Soieniifie CM, Savile Bow, W. 

* B. S. Newall, Esq., F.B.S., Femdene, Gateshead. 

* Francis Murray Newton, Esq., Barton Orange, Ihunton, 



Frederick 
John 
♦ J.W. 
Charles 



W. D. 

Capt. Andrew 
Thomas S. 
♦ Capt. William 



Newton, Esq., BiU Side Lawn, Homsey Lcyne, N, 
Newton, Esq., Sailors' Homo, Doeh Street, B, 
Nichol, Esq., 24 Findhom Place, Edinhwrgh, 
Niven, Esq., M.A., Professor of Mathematics, 

QueofCs CoUege, Corh. 
Niven, Esq., M.A., Trinity CoUege, Cambridge, 
Noble, F.B.S., Jestnond Bene, Neweastlo'Of^Tgno, 
Noble, Esq., Lendal, Yorh, 
Noble, Forest Lodge, Maresfiold, Sussex. 
Lieat.-Col. Wm. Hatt Noble, B.E., Bogal Arsenal, Woolwieh. 

* John Nottingham, Esq., M.D., 18 Bosoommon Street, 

Liverpool, 

* Ankitam Venkata Norsinga Bow, Doha Gardens, Vhagajmtam, 

India, 

* Adm. Erasmus Ommanney, C.B. F.B.S., 6 Iklbot Square, W. 
Bev. Wm. Lake Onslow, M.A., Sandringham, NoffoU^ 
William Osborne, Esq. 

{ Jolins Fage> Esq., 63 South Street, Oreenwioh, &E. 

Major H. S. Palmer, B.E., Barbadoes. 

Bev. James Parkes, Camborne, Cornwall, 

* Bev. Stephen Parkinson, D.D. F.B.a, St. John's College, Cam- 

bridge. 

* John Pamell, Esq., Bddham Bouse, Upper Clapton, E. 
Lieat.-CoL B. Mann Parsons, B.E. F.B.S., Ordnance Survey 

Office, Southampton. 

* Bobert Pearoe, Esq., Ckuroh Court Chamhers, Old 

Jewry, S»C. 



FELLOWS OF THE 80CISTT. (June 1877O 



«S 



lS74,ApT. 10 

1849, Jan. 13 
1867, PeK 8 

1850, Feb. 8 
1870, May 13 
1869, Apr. 9 

1845, Apr. II 
1870^ Jan. 14 
1865, Nov. 10 

1865, June 9 
1869, Feb. 12 

i860, Not. 9 
1859, May 13 

1872, June 13 

1876, Feb. II 

i860, Kay II 

1865, Jan. 13 
1854, Jan. 13 
1872, Apr. 12 

1856, June 13 
i85i,Feb. 14 

1857, June 12 

1874, ^pi** 10 
1849, Apr. 13 

1866, June 8 

1874, ^7 8 
1856, Nov. 14 

1865, Jan. 13 
1863, ^ov» 13 

1866, Jan. 12 
1849, Feb. 9 



Bey. James Peanon, Vleturmfey lUet nm d^ Lmmeaikirt. 

* BeT. Ji^m Newton Peill, B.D., XewUn Tiwy Be(t4fiy, S aRi h u ry. 
F. Cranmer Fenroae, Eaq., MjL, OMy ISeU^ WiwMed^mj 

&W. 

* Heniy Perigal, Eaq., 9 Kifrtk Oe$etmt^ W.C 

* J. Dyson Perrins, Eaq., Dwrenkam Banh^ Mdhpem, 

^ Bey. Stephen J. Perry, F.B.a, Stom^hunt QtUege^ WlaUey, 

Laneoikire, 

* William Peters, Esq. 

* J. E. Hnnter Peyton, Esq., 108 Marina^ St, Leonard*, 
Lamenoe Baxnett nullips, Esq., 41 Warwick Boad, Maida J9tU, 

W, 
Pigott, Esq., AHngUm PigatU, Camhridge$k%re. 
Pigott, Esq., M.D. F.B.S., Hartley Qmrtt near 

Beading, 
Pihl, Esq., (^ristiani^h Norway, 
Pinches, Esq., Ph.D. K.A., &c., OromweU Bead 

West, 8,W, 
Plant, Esq., JRnggtony Oaimiy Queemland, 

AuitraUa, 
Plmnmer, Esq., M^A., Orwell Park Ohtervatory, 

Ipmeieh, 
Pogson, Esq., Director of the Obseryatory, 

Madnu, 

* Bey. T. Johnson Potter, M.A., Ckritt'i Hoipitalf London^ E,C, 

* Eyre Burton Powell, Esq., Madras, 

Henry Pratt, Esq., 18 Preston Street^ Brighton, 

* Bev. Bartholomew Price, M.A. F.B.8., if 8t. Giles\ Osrford, 

* Charles Greville Prideaoz, Esq., 4 Brick Court, Temple, E,C, 

* Charles Leeson Prince, Esq., Observatory, Crowborough Beaeon, 

Tunbridge Wells. 
Pringle, Esq., Mangalore, South Canara, India, 
Pritchard, M.A. F.B.S. &c., Savilian Professor 

of Astronomy, 8 Xeble Terrace, Oacford, 
Proctor, Esq., B.A., 2 North Bead, Clapham 

Park Bead, &W, 
Batcll£f, Wyddrington, Bdgbaston, Birmingham, 
Badcliffe, Bart., Budding Park, Wetherby, 

Yorkshire, 
Badford, Esq., M.D., SidmowfU, Sidmouth, 

* Abthub Cowpsb Bantabd, Esq., M.A., Seobetart, 25 Old 

Square, Lincoln s Inn, W, C, 

* Lord Bayleigh, F.B.S., Terling Place, Witham, Essex. 
Bev. William Bead, M.A., Worthing, 



• a. G. G. F. 
G. W. Boyston 

O. 

* Conrad Hnme 

♦ C. F. 
John L 

* Norman B. 



E. Hamilton 
Bev. Charles 

Bichard A. 

Col. C. 
Sir J. P. 

William T. 



I6 

Bate of EtooUon. 
1864, Apr. 8 
1844, May 10 

1871, Jan. 13 
1859, June 10 

1876, Feb. II 

1870, Apr. 8 
1861, Jane 14 

1872, Feb. 9 

1871, June 9 
1874, Jan. 9 
1874, Jan. 9 
1830, May 14 

1870, Nov. II 
1864, Feb. 12 
1874, Mar. 13 

1867, Dec. 13 

1858, Jan. 8 

1866, Apr. 13 

1853, Jane 10 

187 1, Feb. 10 

1835, Jfu^* 9 
1866, Jan. 12 

1869, Feb. 12 

1839, Not. 8 

1876, Not. 12 
1876, Apr. 12 
1876, Jan. 14 
1866, May 1 1 
1869, Jan. 8 
i86o»Apr. 13 

1870^ Apr. 8 



BOYAL ASTRONOMICAL SOCIETY. (Jane 1877.) 



H. 8. 
Josiah 
Theodore 
♦ J. E. 



Bedpaih, Bsq., Sjfd&nhamn 8.B, 
Bees, Esq., 6 Fig- Tree Court, Temple, RC, 
Bibton, Esq., I OldSguare, lAneoUCt Inn, W.C, 
Bichard, Esq., HopeUmdt, Kew 6hrdent Boadf 
XJew* 

* Bev. Walter J. B. Bichards, iSi(. Jlfory**, Wettmoreland Place, Baya- 

fcater, Jv» 
Edward H. Biches, Esq., LL.D., Bireh Qretee PJaee, Wood* 

houte Moor, near Leeds, 

* William Johnson Bideout, Esq., 51 Charles Street, Berkelejf 

Square, W, 
Edward Boberts, Esq., 3 Union Place, Cheewnieh, SE. 

Bev. Archibald Bobertson, 1 2 Lambert Road, Briwton Bill, & W, 

* Dr. J. C. Bobertson, Monaffhan, Ireland, 

Capt. F. C. B. Bobinson, H.Af,S * Cpal,' Paeifie Station, 
t Bev. T. B. Bobinson, D.D. F.B.S., Observatory, Armagh, 

George Farrer Bodwell, Esq., Marlborough CoUege, WiUs, 
Bev. Henry Boe, Poyntingtim, near Sherborne, Dorset, 

Bogerson, Esq., F.B.O.S., .Sm^A Cottage, Colder' 

stones Bead, AUerton, near Livofpoek 
Bosse, B.A. D.C.L. F.B.S., Birr Castle, Parsons- 
town, Ireland, 
Bottenburg, C.B., Aeaeia Lodge, Kenoimgton^ 

Bath, 
Boath, Esq., M.A. F.B.S., ^ Peter^s OsUege, 

Cambridge, 
Bozborgh, Esq., M.D., 31 St, C^thbori Street, 

Bedford, 
Bassell, Esq., Observatory, Sydney. 
Batter, Esq., Black Book, Brighton, 

* Thomas Glaasebrook Bylands, Esq., IRghfields^ TheUeaU, near 

Warrington, 
Thomas Byle, Esq., 4 Devonshire Plaocy Butboume, 

* General Sir Edward Sabine, K.C.B. B.A. F.B.a| See,, 13 Ashley 

Place, Westminster, S W. 

Herbert Sadler, Esq., Bbniton Beetory, Devonshire, 

* Sir David L. SsLiomoiis,BaTt,,B,A,,Broomhill,TunbridgeWells, 
Harris C. L. Saunders, E8q,,Leacroft House, Staines,Middlesew, 
James Ebenezer Saunders, Esq., F.G.S. dcc.,9 Pinsbwry Cireus,S,C, 
Samuel Saywell, Esq., Collegiate School, Bromsgrove, 
Benjamin Scott, Esq., Chamberlain's Office, OuildhaU, E, C; 

and Heath House, Weybridge, 
George Mitchell Seabroke, Esq., Bugby, 



G. B. 

♦ Earl of 

Col. Baron de 

♦ Edward John 

♦ William 

H C. 
♦John O.N. 



FELLOWS OF THE SOCIETY, (June 1877.) 



17 



Date cf Etoottoo. 
1873, Dec. I^ 
i86i»Jan. 11 
1847, Jan. 8 

1828, Nov. 14 
1857, Jan. 9 

1863, Feb. 13 
1870^ Not. 1 1 
1855, ^^7 " 

1857, Mar. 13 

1851, Jan. 10 
1847, Not. 12 
1866, May II 
1876, Apr. la 
1861, Mar. 8 
1869, Jan. 8 

1861, May 10 

1862, June 13 

1864, Jan. 8 
1861, Apr. 12 

1874, Not. 13 
1876, Apr. 12 

1874, Jan. 9 
1846, Mar. 13 

1871, Mar. 10 

1875, I^®C' JO 

1865, Mar. 10 

1852, Feb. 13 

1868, Mar. 13 

1873, ^^^ J 2 
1852, Apr. 7 

1857, Feb. 13 
185 1, Not. 14 

1874, Dec. 1 1 
1865, Jan. 13 
i867iApr. 12 



James 
William 
Rev. John 
JosiahT. 



Dr. John T. Sercombe, Terrington Lodge, King's Lynn, 

Philip E. Sewell, Esq., Oumeg*t Bank, Norwich. 

♦ Adm. Sir 0. F. A. Shadwell, K.C.B. F.R.S., Meadow Bank, Melk- 

thamy Wilts, 

♦ Earl of Shaftesbury, 24 Oroseenor Square, W. 

♦ Ck)mmander J. M. Share, Seaviow Terrace, Lipson Road, Pfymouth, 
James L. Shuter, Esq., 33 Ihrringdon Street, KC, 
Joseph Sidebotham, Esq., Bowdon, Cheshire. 

♦ BeT. Frederic SilTer, M,A., Norton, near Market Drayion, 

8k/ropihMre. 
Simms, Esq., 138 Fleet Street, E.C. 
Simms, Esq., BerUn ViUa, S/vantnore Boad, Bgde. 
Slatter, M.A., Streatley Viearage, near Beading. 
Slogg, Esq., 242 Stretford Boad, Maneheeter. 
William Thomas Smedley, Esq., 20 Colmore Bow, Birmingham. 
BeT. Maurice Allen Smelt, M.A., Heath Lodge, Cheltenham, 
Alfred Fish Smith, Esq., TraiMng College, Borough Bead, SB, 

Basil Woodd Smith, Esq., Branch E%U Lodge, Sdmpttead 

Booth, N. W. 
DaTid Smith, Esq., 40 Bennett's Sill, Birmingham, 

Capt. Frederick Smith, Trinitg Bouse, NeweaetU-on'Tyne, 
Henry J. S. Smith, Esq., M.A. F.B.S., SaTilian Professor of 

Geometry, BaUiol College, Oxford, 
Smith, Esq., 26 Canonhury Place, Islington, N 
Smith, Esq., The Laurels, Chesterfield, 
Smith, Thruxton Bectory, Hereford, 
Smyth, Esq., F.R.S.E., Astronomer Royal for 
Scotland, &c., Boyal Observatory, Edinburgh. 
Edward Williams Snell, Esq., Kidbrooke House Academy, Shooters* 

Hill Boad, S.E, 
William Philip Snell, Esq., M.A., Belmont, near Havant, 
William Southern, Esq., 6 Dormer Place, Leamington. 

RcT. Thomas Allen Southwood, M.A., Dewerstone House, CheUen- 

ham. 
Spear, St, Stephen'' s Parsonage,Hastings,Calctitta, 
Spence, Esq., 75 Mark Lane, E. C, 
Spottiswoode, Esq., M.A. LL.D. F.R.S., 41 

Qrosvenor Place, S, W. 
Stanhope, Esq., Cannen Hall, Bamsley, 
Stephenson, Esq., 2 Loitdoun Place, Briton 

Boad,S,W, 
Stevens. 

Stevens, Esq., Bhodrons' Hook, near Stirbiton. 
Stewart, Esq., LL.D. F.R.S., Lady Bam Villa, 
Uallow Field, Manchester, 



James 

John Bagnold 
Rev. T. T. 
Charles Piazzi 



Rev. Joseph 
J. Berger 
William 

W. W. S. 
J. W. 

Capt. G. R. 
Robert Norton 
Balfour 



i8 

DafeeolBleetion. 
865, Nov. 10 
864, Jan. 8 

861, Jan. II 



860, Feb. 10 

867, Nov. 8 

861, Jan. II 

869, Mar. 12 
854, Nov. 10 

851, Apr. II 
876, Feb. II 
87s, Feb. 12 



822, Dec. 13 

863, Dec. II 
871, Nov. 10 

875, May 14 
845, June 13 

873, Jan. 10 
855, June 8 

874, Nov. 13 

875, May 14 

868, Nov. 13 
875, Feb. 12 

864, Apr. 8 
850, Jan. 1 1 

870, Apr. 8 
855, Jan. 12 

873, Apr. 9 

874, Jime 12 
854, Feb. 10 



ROYAL ASTRONOMICAL SOCIETY. (June 1877.) 



Dr. Charles 
Lieat. A. W. 



♦ Edward J. 



Stewart, LL.D., Ackender Souse, Alton, Hants* 

StifEe, late of H.M. Indian Navy, Manora, 
HolUH>gton Park, St. LwnardS'On-Sea, 

Stone, Esq., M.A. F.R.S., Her Majesty's Astro- 
nomer, B4iyal Observatory, Cape €f 6f6od 
Hope, 

Stoney, Esq., M.A. F.R.S., Weston, Dundrum, 
Co, Dublin, 

Story, Esq., 88 Oldfield Road, Stoke Newinffton, N, 

Stotfaard, Esq., M.D., Laurel Lodge, Monkstonm, 
Co, Ihtblin, 

Strahan, R.E., India, 

* Wadham Lock Sutton, Esq., Roseway House, Great BerJnump* 

stead, 

* Rev. Sam. Kirke Swann, M.A., Carlton, near Nottingham, 
Edwin John Sykes, Esq., 5 The Quadrant, Buxton. 

Lieut. Jelinger E. Symons, RJT. F.R.G.S., 6 Lansdown Terrace, 

Cheltenham, 



* W. H. Fox 



* G. Johnstone 

♦ Edwin 
John M. 

Capt. George 



Talbot, Esq., M.A. F.R.S., kc, Lacoek Abbey, 

near Chippenham, 
Talmage, Esq., Observatory, Leyton, Essex. 
Taylor, Esq., The Foplars, Avenue Bead, Regent's 

Park, N, W, 

♦ Henry Martyn Taylor, Esq., M.A., Trinity College, Camhridge, 

Taylor, Esq., Warwick House, Warwick Place, 

Grove End Road, N,W, 
Tebbutt, jun., Esq., Windsor, New South Wales, 
Tennant, F.R.S., H,M,S Mint, Calcutta, 
Terby, Rue des Bogards, Louvain, Belgium. 
Silvanus Phillips Thompson, Esq., B.A. B.Sc., i St, Mary's, York; 

and University College, Bristol, 
Thomson, M.A. LL.D. F.R.S., College, Glasgow, 
Thomthwaite, Esq., 416 Strand, W.C, 
Todd, Esq., C.M.G., Observatory, Adelaide, 
Todhunter, Esq., MJL F.R.S., Bourne House, 

Cambridge. 
Tomlinson, Esq., King's CoUege, W.C. 
Tomlinson, Esq., Grove Lodge, York, 
Tomlinson, Jan., Esq., Auckland College, New 

Zealand, 
Tompkins, Drayton House, Shaftesbury Road, 

Southsea, Hants, 

♦ Captain Henry Toynbee, 12 Upper We$tbowrne Terrace, IT. 



Charles G. 
♦ Harry 



X Thomas 

John 

Colonel J. F. 
♦ Dr. Francois 



• Sir William 
W. H. 
Charles 

* Isaac 

Herbert 
William 
William 

Rev. C. R. 



FELLOWS OF THE SOCIETY. (June 1877.) 



19 



i87i» Haj la 
1863, Hay S 

i84cs Dec. II 
1853, May II 
i864«NaF. II 



1867, Apr. 12 
1856^ Jan. II 

1867, June 14 
18539 Jan. 14 

1868, Dec. II 
1855, Apr. 13 



1849* Jao- *I2 
1876^ Feb. II 

1858, Jan. 8 



1863, Jan. 9 
1867, Kar. 8 
1872, Feb. 9 
1850, Jane 14 
1863, Feb. 13 

1876, Jan. 14 
1867, Jan. II 
1876, Dec 8 



1837, Kay 12 

1873, May 9 
1851, Dec 12 

1874, Nov. 13 

1870, Mar. 1 1 
1857, Xov. 13 

1876^ Apr. 12 



Clarence Ed. 
* Oapt.G.Lyoii 

George 

Thomas 

Edward 



Trotter, Esq., 34 J^^ew Bridge Street, E,C, 
Topman, ILM.A., i Vanbru^h Park, JBlaoJtheathy 

8.E. 
Tumbnll, Esq., Bow HiU, Abbots Langleyy Herts, 
Tomer, Esq., M JL., 36 Ha/rley Street, W, 
Tyer, Esq., 15 Old Jewry Chambers, E.C,; and 

32 Russell Square, W,C, 



* Frederic R. H. Varley, Esq., JiRldmay Street, Highbury, iV. 
Bev. George Yenables, Vicarage, Great Yarmouth, 

* Commander E.H. Yemey, BJ7., Bhianva, Bangor, North Wales. 
George Yenables Vernon, Esq., i Osborne Place, Old Trafford, 

Manchester, 
David Vines, Esq., Hope Villa, Clifton Wood, CUfton, 

Wm. Beynolds Vines, Esq., Care of 8. H. Vines, Esq., Christ's 

College, Cambridge, 



A. Diedrich 
John May 

Charles V. 



Col. J. T. 
M. M<Neal 
George 
* Marcus 



Wackerbarth, Esq., Observatory, V^fsala, 
Walden, Esq., The Observatory, York Street, 

Jersey, 
Walker, Esq., F.R.S., Hon. Mem. Horo. Inst., 

Fast Pres. Soc. Tel. Eng., Fernside, Bedhill; 

and Scientific Club, Savilc Bow, W, 
Walker, R.E. F.R.S., India, 
Walker, Esq., 5 Cecil Place, Glasgotv, 
Wall, Esq., Portlajid House, Clevedon, Somerset. 
Warburg, Esq., 2 Bishopsgate Street, B.C. 
Lieut- Col. M. Foster Ward, Banncrdcmn House, Bath Easton, 

Somerset, 
Wardell, R.A., Waltham Abbey, Essex, 
Warner, Esq., 47 Sussex Square, Brighton, 
Waterhouse, Bengal Staff Corps, Assistant 

Surveyor-General, Surveyor- GeneraVs Office, 

Calcutta, 
Waterhouse, Esq., F.R.S., Halifax, Yorkshire, 
Waters, Esq., 24 Ladbrohe Square, W, 
Waterston, Esq., 28 Gay field Sqttare, Edinburgh, 
Wathcrston, M.A., Warley Bead, Brentwood, 

Essex, 

♦ Rev. Hy. Charles Watson, M.A., Clifton College, Clifton, 

♦ John Watson, Esq., Scaham Chemical Works, Sunder- 

land, 
Thomas Watson, Esq., J.P. F.B.G.S., Cape Town. 



* Major W. H. 

* Thomas 

* Captain James 



♦ John 
Sidney 

♦ J.J. 

Rev. A. Law 



20 



ROYAL ASTRONOMICAL SOCIElTX'. (June 1877.) 



Dale of BlMtkm. 
1834, Nov. 13 
1867, Apr. 13 

1852, Jan. 9 
1864, Feb. 12 
1875, June II 

1 8491 Jan. 12 
1877, Jan. 12 
1872, Apr. 12 

1849, Jan. 12 



1845, June 13 

1869, Jan. 8 
1877, Feb. 9 

1845, Jane 13 
1872, Dec. 13 

1852, Nov. 12 
1865, May 12 

1865, Dec. 8 

1870, Jan. 14 
1872, June 14 

1868, Jan. 10 

1866, Nov. 9 
1875, Dec. 10 

i860, Mar. 9 
i87S»Apr. 9 

1872, Jan. 12 
1874, J^uie 12 

1869, Dec. 10 

1836, May 13 
1861, Dec. 13 

1837, Jan. 13 
1856, Mar. 14 



♦ Rev. S. W. 
Sir A. Scott 



* Samuel Ghas. 



Waud, M.A., Bettendefh near WieVord^ Essex, 
Waagh» K.C.B. F.R.S., 7 Petenham 7\nraee, 
South XenHn^toHj W, 

♦ Rev. Thomas Wm. Webb, A.M., Bdrdwiek Partonage^ Hereford, 
Richard Webster, Esq., 5 Queen Vtetoria Street, B,C, 
Francis Richard Wegg-Prosser, Esq., M.A., Belmont^ Hereford ; 

and 84 Eoeleiton Square, & W, 

♦ Rev. Alfred Weld, B.A., San Girolamo, Fieeole, Florence, 

♦ Ck)mmander W. J. Lloyd Wharton, HM, Surveying Ship, *Ihmn.* 
G. M. Whipple, Esq., Kew OUervatory, JHehmond, 

Surrey. 

Whitbbbad, Esq., F.R.S., Tbbabusbb, Brewery, 
ChimeU Street, B.C ; and SouthiU, Biggles- 
wade. 

White, Esq., F.L.S., West Drayton, 

White, Esq., Observatory, MeWoume, Australia, 

White, Esq., 13 Bolton Gardens, South Kensing- 
ton, S.W. 

\^^ite, Esq., Killingworth, Neweastle-on-Tyne. 

Whitehonse, Esq., Bown Place, HaHing, Peters- 
field. 
Rev. Charles W. Williams, D.D., Mfrth London Collegiate School, 

High Street, Camden Town, N. W. 

Williams, Esq., 16 Cambridge Terrace, Hyde 
Park, W. 

Williams, Esq., M.A., 37 Bedford Bow, W.C. 

Williams, 42 Oxford Street, Southampton, 

Williams, Esq., Belmont, Twioketiham. 



t Alfred 
* Edward John 
John Sidney 

{ Thomas R. 
E. 0. W. 



George 

♦ Harry Samuel 

♦ Capt. John 
W. Mattien 



Rev. Wm. Owen Williams, 89 Berkeley Street, Liverpool, 

Wilson, Esq., M.A., Rugby School. 
Wilson, Esq., Baramona, Streete, BathoweH, 

Ireland. 
Wiltshire, 25 Granville Park, Lemisham, S.E. 
Winstanley, Esq., The Bootor's Cottage Black- 
pool. 
Winter, Esq., Madras Bailway, India. 
With, Esq., The Laboratery, Model and Experi- 
mental Farm, Hertford. 
Wood, Esq., Wliaffedale College, Boston Spa, 

near Tadcaster. 
Woolhouse, Esq., A Iwyne Lodge, Canonbury, y. 
Baron Henry de Worms, South Lodge^ Rutland Gate, S. W. 
Maj.Gen. W. K. Worster, 7 Woodlands Jlllas, Blackheath. 



J. Maorice 
♦ William E. 

Rev. Thos. 
David 

G. K. 
G. H. 

John 

W. S. B. 



Hale 



Wortham, Esq., Boyston, Herts. 



1877, Feb. 9 
1862, Jan. 10 
1842, Msr. 1 1 

1867, Apr. 12 
1840, Feb. 14 
1862, Dec 13 

1875, June n 



FBLLOWS^OF THE SOCIETY, (June 1877.) 



SI 



* A Mason Worthington, Esq., B.A., Clifton CoUfige, Clifton. 
William Wray, Esq., Laurel House, North HiU, Highgate, 

* Bev. Dr. Alfred Wrigley, 67 High Street, Clapham, 8, W. 



Stephen M. 
♦ Colonel W. 
Sir Allen 



Teat^ Esq., 2 Orqfton Street, DubHn, 
Tolland, R.E. F.B.S., 14 i^. Stephen's Square, W, 
Toung, I St, Jameit Street, S. W. 



Prof. Chas. Venoeslas Zenger, VtUa Ze^ieek, Weinberggemeinde, 

Pott Zxzhow, bei Prague, 



ASSOCIATES. 



Dtte of Election. 






• 


1866, May II 


G. F. J. Arthur 


Auwers, 


Berlin. 


1844, Dec. 13 


Gaetano 


Cacciatore, 


Pdlemio. 


1848, May 12 


Thomas 


Clausen, 


Darpat. 


1850, Dec. 13 


Annlbale 


DeGasparis 


, Naple$. 


1848, May 12 


Herv6 A. E. A. 


Faye, 


Paris. 


1866, May II 


Wilhelm 


Forster, 


BerUn. 


1848, May 12 


Johann Gottfried 


Galle, 


Bretlau. 


1822, Jan. 1 1 


Alfred 


Gautier, 


Geneva. 


1855, Jan. 12 


Benj. Apthorp 


Gould, 


Qtrdava, Argentine 
BepuhUc. 


1874, Jan. 9 


Eduard 


Heis, 


Muntter. 


1872, Nov. 8 


Jules 


Janssen, 


Paris. 


1848, May 12 


Karl Friedrich 


Enorre, 


Nieolajew. 


1863, Nov. 13 


Marian 


Eowalski, 


Kazan. 


1837, May 12 


Johann 


Tiamont, 


Munich, 


1847, Jan. 8 


Urbain Jean Joseph 


Le Verrier, 


Paris. 


1853, Apr. 8 


Karl Ludwig von 


Littrow, 


Vienna. 


1864, Nov. II 


Eduard 


Luther, 


Kmigsberg. 


1854, June 9 


Earl Theodor Robert 


Luther, 


Bilk. 


1874, Nov. 13 


Axel 


MoUer, 


Lund. 


1872, Nov. 8 


Simon 


Newcomb, 


Washingt4>n. 


1872, Nov. 8 


Hubert A. 


Newton, 


Conneetic\tt. 


1874, Jan. 9 


Theodor 


Oppolzer, 


Vienna. 


1850, Apr. 12 


Benjamin 


Peirce, 


Camhridge, U.S. 


1848, May 12 


Christian A. F. 


Peters, 


Kiel. 


1844 Apr. 12 


Emile 


Plantamour, 


Geneva. 


1872, Nov. 8 


Lorenzo 


Bespighi, 


Borne. 


183s, Apr. 10 


Otto August 


Bosenberger, Halle, 


1872, Nov. 8 


Lewis M. 


Butherfurd, 


New York, 


1866, May II 


Truman Henry 


Safford, 


Chicago, 


1825, Mar. II 


Giovanni 


Santini, 


Padua. 


1872, Nov. 8 


G.V. 


Bohiaparelli, 


Milan, 


1874, Jan. 9 


Johann Friedrich Julius Schmidt^ 


Athens, 



ASSOCIATES OP THE SOCIETY. (June 1877.) 



23 



DAteoCSkctton. 
1853, June 10 
1S48, Hay 12 
1853, Jane 10 

1863, Nov. 13 

1874, ^^^^ 9 

1864, Nov. II 
1845, Jan. 10 

1872, Not. 8 

1873, Nov. 8 



Angelo Secchi, Some, 

Otto von Stmve, Poulkova, 

Yvon Villarceaa, Paris, 
Friedrich Aug. Theodor Winnecke, Strashurg, 

C. Wolf, 

Bndolf Wolf, 

Baron Fabian Jacob Wrede, 



C. A. Young, 

Johann Karl Friedrich ZeUner, 



Parii, 

Zurich, 

Stockholm. 

Dartmouth CoUegetU.S, 

Leipzig, 



LOSDOV I PRISTBD BT 
■tW I M W O OP* AVD CO., XBW-tTmBST SQCABl 

idw rABUAMnnr tnwm 



MONTHLY NOTICES 

OF THE 

ROYAL ASTRONOMICAL SOCIETY. 

Vol. XXXVII. Novbmbbe io, 1876. No. i. 

William Huggiks, Esq., F.B.S., President, in the Chair. 

Georee Spedding Almond, Esq., Daisy Hill, Dewsbarj; 
JofliaA Owen Corrie, Esq.,B.A., Bed Cot, Putney Park Lane ; 
Capt. Joeepli Leeman, Aberdeen ; and 
Herbert Sadler, Esq., Hbniton Bectorj, Deyonshire ; 

were balloted for and duly elected Fellows of the Society. 



Xoie an a Method of obtaining Equatoredl Motion by meam of a 
simple addition to an Altazimuth Stand. By Lord Lindsay. 

If we take a telescope mounted with vertical and horizontal 
motion, these may be converted into equatoreal motion by the 
addition of a bar of metal or wood. 

At any convenient distance below the altitude axis of the 
instrument let a bar be fixed at right angles to the pillar or 
azimuth axis. In the bar there should be a "N^shaped slot, through 
which a string or wire may slide, and be clamped by a screw 
pressing it into the angle of the V. 

Let the bar project in the plane of the meridian to such a 
distance that the angle contained between the bar and a line 
drawn from the V-shaped slot to the centre of motion of the 
altitude axis is equal to the latitude of the place of observation. 

In other words, let the distance of the angle of the V-shaped 
slot from the central line of the pillar of the instrument be equal 
to the distance from the upper side of the bar to the centre of 
motion of the altitude axis multiplied by the cotangent of the 
latitude of the place of observation. 

^ The object-glass end of the telescope should now be connected 
with the V-shaped slot by means of a line wire or string, and a 

▲ 



2 Lord Lindsay J Note on obtavnmg Equaioreal Motion, xxxm. x, 

weight may be attached at the other end of the telescope, in 
order to keep the wire always stretched. On moving the tele- 
scope while the wire remiEdns clamped it will be foond, as is 




o 

A Stand. 

C Table. 

E ControUing Ha*. 

Angle DOBBLatitnde of place. 



B Cotro of Alt. notieiL 

DK Bod. 

K Pinohiag ecrew to damp-Unt E. 

M Weight to keep E tight 



evident, that the telescope can only move in a parallel of decli- 
nation. If it is wished to follow another star, the wire must be 
onclamped and the telescope re-set. The eqnatoreal motion thus 
produced will be found to be quite sufficiently accurate for all 
ordinary purposes. 

The method is so simple that I think it must have occurred to 
other persons ; but as I have not seen any account of it in print, 
I have thought that it might be worth while to mention it to the 
Society. 

Note. — Since writing this paper, my attention has been drawn 
to the fact that Sir George Airy, in the 15th vol. of the Monthly 
Notices, has described a mounting for a large telescope on this prin- 
ciple ; with the difference that he placed the point of attachment 
of the cord to the north instead of to the south of the telescope. 



Bb?. 1876. Mr. ThomihuHiiie^ Improved AUamMdh Stand. 3 

IW^^ of an Improved Alkunmuth Stand for BefiecUng 
Tdeseopesj with a new Form of Binocular Eyepiece. By 
W. H. Thornthwaite. 

Hftymg been requested by Mr. H. Alers Hankey, of Qneen 
Aim's Huisions, to provide some form of Binocular eyepiece 
opeciany applicable to telescopes of large aperture, sncn as 
tne i2^mcli Eqnatoreal, with nlyered glass mirror, which my 
^were oonstoncting for him, seyeral experimental eyepieces 
Q^ TBrions forms were tried, and also a considerable amount of 
time and bought deyoted to the subject of Binocular yision in 
oomiedion with the telescope. I hope a short account of these 
experiments and their ultimate results may proye of interest to 
the PeDows. 

There are two important adyantages to be obtained by Bino. 

eolar yision, the first being, as the name implies, the employment 

^ both eyes, instead of confining observation to either the right 

or left eye ; the second advantage consists in the apparent 

(tereosoopic eff*ect produced when both eyes are employed. In 

'eipeot to the first-mentioned advantage, it will be admitted 

im the constant use of one eye must, fliter a time, be injurious 

hoth to that employed and also to its fellow. To take an extreme 

CBse, it is found that a single spectacle lens considerably injures 

the sight; the eye which is not assisted by the glass becoming 

after a time of a different focus to the other. But when boin 

eyes are brought into action no such unpleasant results accrue ; 

and as the observer discontinues his telescopic work, he finds his 

eyes are not nearly so fiatigued by long-continued gazing as they 

▼onld haye been if only one eye had li^n used. 

Secondly, it is impossible that any real stereoscopic effect can 
be noticed in yiewing objects so distant, but it may be asserted 
that a considerable apparent effect is produced by Binocular 
vision. The rotundity of the Sun and Moon, and the moun- 
tainous surface of the latter, stand out in bold relief; Jupiter and 
Scdum appear eurrownded by their Satellites, and not, as in an 
ordinary eyepiece, as a flat picture. 

Haying made these few general remarks on Binocular yision, 
I beg to append my own experience, and a short description of 
the eyepiece now exliibited. 

The first eyepiece tried was an ordinary Binocular microscope, 
with an extra large " Wenham" prism. Except on the Moon, 
this form was found to be very trying to the eyes, on account of 
the strain put on them in order to make the two dull fields of 
the eyepieces coincide : using this form for a few minutes occa- 
sioned considerable giddiness. No such yisual strain is experi- 
enced with a Binocular microscope in its ordinary employment, 
as the fields are much brighter, and therefore more easily made 
to coincide. Seyeral other plans of dividing the cone of rays 
were tried without much success, the great difficulty being that 
the diyision must occur so close to tho eyepieces, that their 

A 2 



4 Mr. Thcmthwattey Improved AUannmUh Stand. xzxYn. !» 

fields, wiih even moderately low powers, were only partially 
iDiimiiiated. 

The Binocular now exhibited has neither of the preceding 
defects, the fields of low-power eyepieces being entirely illa- 
minated, and it can be nsed for any length of time withoat 
tiring the eyes. Its principal disadyantage is the loss of light 
occasioned by sereral reflexions, bat as with even moderately 
large telescopes, the light of the Moon and of some of the planets 
is excessiYe, especially to sensitive eyes, this defect mnst 
sometimes be an advantage. I may here remark, that I am now 
constmcting a Binocular on a somewhat similar plan, but sab- 
stitnting prisms for silvered flats, and in which therefore the 
loss of Ught will be very small. 

The principle of this instroment is very simple, and is as 
follows: — The rays of light from an object-glass or specahim 
fidl on a silvered glass, placed at an angle of 45°, from this they 
are reflected 1^ an angle of 90° to another silvered glass, paraUel 
to the first, and thence to one eyepiece. But the first reflecting 
snr&ce is an exceedingly thin coating of silver on a glass with 
parallel sides; a portion of the light is therefore transmitted 
through the transparent silver film, and then by two more sil- 
vered glasses it is reflected to the other eyepiece. The object of 
silver film is to avoid the secondary image which would be 
reflected from the inner side of the glass. The eyepieces are 
therefore side by side, and have their optical axes parallel; direct 
vision with each eye is thus obtained. The eyepieces have each an 
independent focussing slide, and they can be separated to accom- 
modate diflerent observers whose eyes may be various distances 
apart ; this separation is affected by the miUed head, the screw on 
one side of which is right-handed, and on the other left-handed ; on 
revolving the milled head, therefore, the eyepieces are separated 
or brought nearer together. If solar or first surface prisms were 
used for the several reflexions, the instrument would form a 
Binocular for observations of the Sun. 

The Scinch Alta2dmuth on which the eyepiece is now shown, in 
order that the Fellows may roughly test its binocular performance, 
has been constructed with several important improvements. I 
will merely call attention to them in order that the Fellows may 
practically test their utility. 

The open tube now adopted is so made that it shows that any 
closed tube may be similarly altered. The altitude clamp is of a 
novel kind, and is brought for convenience close to the eyepiece. 
Lastly, the screw motion in azimuth is continuous throughout 
the entire circle, or may be at pleasure thrown out of gear. 

1876, A'or. 9. 



Nov. 1876. Trof, Langley^ On Direct Effect of Sun-tpots etc, 5 

Mecuurement of the Direct Effect of Su/n-spots on Terrestrial 

OUmates, 

By Prof. S. P. Langley. 
(Commumieated by E. Dunkin, F.B.8,) 

Since the qnestion of the inflnence of Solar changes on Ter- 
restrial climates was opened by the elder Herschel, a great 
number of Meteorological observations have been tabulated and 
diBcnssed without the apparent attainment of any conclusive 
result, nor does there seem to be immediate hope of any solution 
from the study of such Terrestrial effects, while the evidence 
from these bears so different a meaning according to the inter- 
pretstion of the compiler. 

Though complete knowledge on this point seems still &r 
beyond our reach, yet, if we consent to limit our enquiry to the 
direct effect of Sun-spots on the heat the Earth receives, there is, 
it seems to me, an untried means, which yields a sufficiently 
exact solution of the problem. It appears possible at least, to 
show (within certain definite limits) by how many degrees or 
parts of a degree Centigrade the Earth's mean annual temperature 
necessarily varies between a year of maximum and a year of 
TniTtimnTn Spot-arcas SO far as the immediate effect of these on the 
solar thermal radiation is concerned. 

To do this it is necessary, — 

(i) To procure from experiment trustworthy measurements 
of the relative amounts of photospheric, penumbral, and umbral 
radiation. 

(2) To determine the relative photospheric, penumbral, and 
umbral surfaces, in a maximum and in a minimum year, and 
(having suitably combined these data) to 

(3) Show within what specific limits we can assert that the 
Terrestrial temperature will be necessarily changed. 

The first condition, is so far as I know, heretofore unsupplied, 
owing to the experimental difficulties which have only lately been 
overcome. The results of recent measurements at the Allegheny 
Observatory now published for the first time will furnish these 
data. 

For the second condition, I shall avail myself of the 
published results of Schwabe, Carrington, De La Rae, and others. 

For the third, a method will be employed which, if in some 
measure novel, is apparently a legitimate deduction from facts in 
themselves not open to question. 

1. Direct Tkennal Measurements of Solar Radiation. 

Since the original observations of Henry, in 1845,* established 
the important fact that the thermal radiation of a spot is in general 

• LoncUm, Edinfmrghy and Dublin Philosophical Magazine^ 3rd Scries, 1846, 
p. 330; Poggendorfs Annalcn^ 1846, vol. 68, p. 102. 



6 Troj. La/ngleyy On Measnr&mmt of Direct Effect zxxyil x, 

leas than that of the photosphere, nothing appears to have been 
added to show by how much it differs. If quantitative results 
have, in spite of their obvious value, never been obtained, it is 
doubtless owing to the experimental difficulties we meet in pass- 
ing from the point at which we can say that the spot-radiation is 
less, to that at which we can say with confidence how much it is 
less. To but partially indicate the nature of these difficulties, 
we may observe that the umbra of a sun-spot occupies so sihall 
an area, that the quivering of the telescopic image, due to atmo- 
spheric tremor, commonly causes its libration through a range on 
either side of its mean position exceeding its own semi-diameter. 
"Whatever the size and stability of the telescope, or whatever the 
enlargement of the image, or the minuteness of the thermopile 
we seek to expose only to umbral heat, penumbral radiations will 
then be registered to some extent, or if it be penumbral radiation 
we would observe, umbral and photospheric neat will alternately 
enter with it. This is no serious drawback, if we seek to show 
only, that the spot as a whole is cooler or hotter without enquir- 
ing in what degree ; but obviously it is fatal to accuracy, when 
we would determine by how much the radiation is diminished by 
each part. We must either take the telescope beyond the limits 
of our lower atmosphere then, or observe only in those rare and 
brief periods when the image is still. These periods in our 
northern climates are always associated during the day with the 
presence of moisture and haze in the atmosphere. It is almost 
superfluous to remark that these conditions, which secure a 
tranquil image, are precisely those most un&vourable to the 
transmission of radiant heat, and the excessively diffuse and 
enfeebled rays which form the enlarged image, are, in spite of 
every precaution, apt to be confused with radiations which reach 
the pile from exixaneous sources. 

Trials were made in 1873 and 1874 of a great many plans, for 
so shielding the pile that it might be absolutely protected against 
every source of disturbance except the minute pencil of umbral 
or penumbral rays, with incomplete success, till in the close of 
the latter year an apparatus was devised by the writer with 
which, though the time for large spots was passed, satisfactory 
measures were at last obtained. 

The apparatus cannot be fully explained without illustration ; 
the essential conditions of success, however, are that to an eye 
placed in the position of its working face the part of the spot to 
be studied and the blackened walls of a chamber surrounded by 
water at a constant temperature are alone visible, and that pro- 
vision is yet made for the observer's ability to verify at any 
moment the position of the image projected on this hidden face, 
which is maintained at all times in the optical axis. The pile 
specially constructed by the late Mr. Becker is composed of very 
minute elements and used in connection with a reflecting galva- 
nometer. The use of a large Equatoreal with accurate clock-work 
is of course presupposed. That employed was a refractor (and 



Not. 1876. 0/ Sun-ipoU on TerrestrM OUmaies. 7 

it wOl hence be understood that our measurements are confined 
to Inminons heat rajs), haying an aperture of T3 inches. 
The pnnected image was formed on a scale of from fonr to eight 
feet to tne solar diameter. 

The pile was ordinarily first placed in the image of the 
photosphere, between the spot and the centre of the disk, and 
the galyanometric deflexion noted ; next an exposore of equal 
in the nmbra was made, and then the observation once 
more repeated with the pile in the adjacent photosphere between 
tiie spot and the limb. The mean of the photospheric readings, 
after the instrumental reductions are applied, is used as a divisor 
for the (reduced) umbral reading. The quotient eroresses the 
value of the umbral radiations, in parts of those of the adjacent 
photosphere. The decrement of heat, as we approach the limb, 
IS, thooffh not exactly, yet so very neaHy, in tiie same ratio for 
photosphere and spots, that no correction is needed on this 
account for the present observations. Thirty-six measnrements 
on TJmbriB, and thirty-two on Penumbne, were obtained in the 
iutumn of 1874 and the spring of 1875, as follow : — 



Uintanl Haat-rsdlBtlon 


PennmbnJ Heat-ndUtkm 
(FhotoiplMric Badifttionsi'oo). 


0-55 


0-86 


0-43 


074 


0-49 


0*93 


049 


0*98 


0-55 


0'8o 


0*61 


0-68 


0'6i 


082 


0*53 


080 


055 


084 


063 


073 


0-57 




0*50 


074 


0-49 


083 


o*53 


0-84 


0-54 




049 


075 


053 


073 


057 


084 


0-57 


079 


o'6x 


0-69 


0*52 


071 


0-49 


o*8i 


0*51 


077 



8 



rroj, lAmgleffy Un Measut 


ement oj Ihrei 


yt JS^ect xxxvn 


Umbnl Heat-ndiatioii 
(Plioloipherio BadUtionssfoo). 


Fenomtaral Hcftt-ndiftUon 
(Fhotospberio B«diatton«x-oo). 


0-54 






059 




089 


054 




083 


0*52 




0*62 


0-47 




082 


0'6o 




074 


053 




074 


047 




082 


052 




074 


052 




096 


054 


« 


089 


054 




089 


0*58 






Mean 0*54 ±005 


Mean 


080 ± O'OI 



The result is, that taking the mean thermal photospheric radiation 
in the spot's yicinitj as unity, the mean Umbral radiation is 
fifty-four one-hundredths (with a probable error of five 
one- thousandths), the mean Penumbral radiation eighty one- 
hundredths (with a probable error of one one-hundredth). These 
errors include all discrepancies due to the greater or less 
approach to the limb in the spots measured, or due to absolute 
differences in their radiation, as well as the errors of observation. 

(2.) Comparison of Unibral and Penumhral Areas in a year of 
maximfium vjith those in a year of minimum. 

To determine the spotted area of the disk in years of maximum 
and of minimum, I have taken from a paper by Messrs. De La Rue, 
Stewart, and Loewy, in the Philosophical Tra>nsactions (' Researches 
in Solar Physics,' No. 2, page 115), the following dates : — 

Maximum Dec. 31, 1836 Minimum Sept 21, 1843 

Nov. 14, 1847 „ April 21, 1856 

Sept. 7, 1859 „ Feb. 14, 1867 






In the same Memoir, under Table 8, is given for every 14th and 
28th day of the month from 1832 to 1868, the total spot-area in 
millionths of the Sun*s visible hemisphere, deduced from the 
observations of Schwabe, Garrington, and the authors ; and, by 
addition of the fortnightly means, we obtain the following annual 
ones for three years of maximum and three of minimum : — 



Not. 1876. of Sun-^pots on Terrettrial CUfnaies, 9 

^'Ld%'rSb.SSS}D~-8.'83. Spot««- .►34670 

Sept. 21, 1843 .. .. 002555 

Nov. 14, 1847 „ „ 031055 

April 28, 1856 „ „ '000850 

Sept. 14, 1859 „ „ 034530 

Feb. 14, 1867 „ „ *oo2ii5 






•005520 100255 

Whence we find the mean spot-area at any time in a year of 
maximfim ss '001392, in a year of minimum = '000077 ? figures 
which are deduced from a large number of spots distributed with 
approximate uniformity in longitude, and which hence represent 
not alone the total spot-area in part of the visible hemisphere, 
but the total apparent area in parts of the visible disk. 

From an enumeration of every Umbral and Penumbral mea- 
surement recorded by the authors, from February 7, 1862, to 
December 31, 1863, we obtain — 

Mean Umbral Area 21371 

mm ''' wm '27 * 

Moan Spot Area 79747 * 

Mean Penumbral Area 58377 
"""Mean SpoTAroa *" 79747 " 

These figures obtained from observations made at a period 
midway between a maximum and a minimum doubtless repre- 
sent with approximate truth the relative Umbral and Penumbral 
areas at other periods. Hence, we conclude that the 

Mean Apparent Umbral Area in a year of Maximum — *ooi 392 x '27 = '000376 
Penumbral „ „ =-001392 x •73 = -001016 

Umbral „ Minimum « 000077 x '27 » *oooo2i 

Penumbral „ „ — 000077 x 73 = 000056 



f« 



If 



We have now to multiply each area by its measured rate of 
thermal radiation already found. Thus, we obtain 

•000376 X '54 a -000203 -00002 1 X '54 = 'OOOOI I 

•001016X -80 «= -000813 '000056 X -So = '000044 



'001016 -000055 

and since it thus appears that the .average spot-radiation earth- 
wards in a year of maximum is 'ooioiG, and in a year of 
minimum '000055 of that of the apparent disk, it follows that 
the total effect of the spots in diminishing the solar radiation by 
the diminished heat from the increased area they periodically 
occupy, will not exceed the difference of these numbers or 



lo Trof, Langl&y^ On MeasuremerU of Direct Effed etc. xxxvn. x, 

'000961. The fignre in the sixth decimal place having no real 
significance, and that in the fifth being doabtfal, we Aaj saj 
that the greatest admissible direct effect of the spots is to 
diminish i£e Son's thermal radiation by a quantity somewhat less 

than — and somewhat greater than — of one per cent. 
10 ° II ^ 

(3) Limits within which Terrestrial Temperature toiU be affected by 

sxich Changes, 

An exact computation of the efiect of the Solar radiations on 
Terrestrial Temperatures requires a knowledge of the heat the 
Earth receives from other than solar sources. A number of 
eminent Physicists have attempted to determine this, but with 
results which are so discrepant that we can feel, as it seems to 
me, little confidence in their use. The method here adopted* 
wiUj not assume any knowledge as to the " temperature of 
space," or any of the other as yet indeterminate &ctors, indis- 
pensable to a complete solution of the problem : we shall there- 
fore not attain an exact result ; but we shall be able to feel con- 
fident that wo can say with assurance within what limits the 
truth must lie. 

There seems to be no question that a temperature as low as 
— 56**C. has been observed in the open air of the Arctic regions, 
and it is plain that wore the Sun's heat altogether withdrawn, 
the mean Terrestrial temperature would iaXL at least as low. In- 
dependently of stellar radiation, the Earth receives at the upper 
limit of its atmosphere a certain amount of heat from non- 
luminous interplanetary matter, which has absorbed and is 
radiating obscure heat originally derived from the Sun. Com- 
putations of the amount of this obscure radiation indicate that 
it is more considerable than might be supposed; but as little 
value attaches (it seems to the writer) to such estimates, they 
are referred to, only to enforce the statement that were the Sun's 
heat wholly cut off, whatever the mean temperature the Earth 
might attain it would certainly bo below — 56^0., and as its actual 
mean actual temperature is estimated at from +14** to +16® 
Centigrade, it is clear that to the entire solar thermal radiations 
not less than 70° G. of our actual temperature is due. 

The least change in solar heat due to the cause we discuss 

being, as has been shown, — of one per cent, of the whole radia- 

10 

tion, whose thermometric effect registered here is a change of at 
least yo^C. we find — i.=o°'o630. as the i^(u^ change in Terrestrial 

temperature which we can attribute to the direct effect of the 
spots. 

Again, since the Earth can in no circumstances part with more 
heat than it possesses, we may, taking the absolute zero as at 



Kcnr. 1876. Mr. TehbuU^ On Solar EcUpse^ 1876, Sept. 17. xi 

— 274® 0. Bay that 16**+ 274**= 290** C. represents the greatest 
effect we can assign to the Snn, and that since the greatest 
change in solar ladiation due to the spots is shown to be less 

than — of one per cent. — ^ = 0^*30 C, is the greatest change 
10 ^ 10 

in Terrestrial temperature which can be due to this cause. 

In all that has preceded it has depended on certain data 
drawn from observations made by means which exclude the 
measurement of the thermal effect due to rays in the ultra-red 
and ultra-violet parts of the spectrum, but were these obtainable, 
there seems no probability that these conclusions would be 
materially affected. 

To prevent misapprehension, let it be repeated that nothing 
is here given as being to the writer decisive of the question — 
whether Terrestrial temperature may not be quite otherwise 
affected by some varying Solar action of which spots are merely 
aooompaniments — and then, with this understanding, we may 
reach the following conclusion : — 

Sun-spots do exercise a direct and real influence on Terres- 
trial climates by decreasing the mean temperature of this planet 
at their maTJTnum. This decrease is, however, so minute, that 
it is doubtful whether it has been directly observed or discri- 
minated from other charges. Its whole effect is represented by 
a change in the mean temperature of our globe in eleven years, 
not exceeding three-tenths, and not less than one-twentieth, of 
one degree of the Centigrade thermometer. 

Allegheny Observatory, Allegheny, Pa,, 
1876, June 16. 



Observations of the Solar Eclipse of 1876, September 17. 

By John Tebbutt, Esq. 

The atmosphere was calm and clear. At the time of first 
contact the Sun was low, but the undulation along the limb was 
not so great as I expected ; this phase was, therefore, pretty well 
observed. The observation of the last contact was very satis- 
fikctoiy. The following are the Observatory local mean times of 
observation : — 

d h m ■ 
First contact Sept. 17 1822 2*6 

Last „ „ 20 I 34*3 

The Sun being hidden from the 4^]nch Eqnatoreal by the 
house and trees, the eclipse was observed by means of the 3:^-inch 
portable refractor armed with a power of ninety and a green 
ihade. The position of the telescope was about sixty yards east 



12 Senor Arcimia^ Observations of (he Lunar Eclipse^ xxxvn. i, 

of the Obseryatorj. Notwithstanding a carefol somtiny, I did 
not sacceed in observing the thorn-like projections of light seen 
on the solar cnsps by Captain Noble and others daring the eolipse 
of September last. The eclipse, which was equal to about one- 
third of the Sun's diameter, had an interesting effect on a black- 
bulb thermometer enclosed in an exhausted glass globe. 

Windsor^ New South WaleSj 
1876, Sept, 21. 



Observations of the Lunar Eclipse^ 1876, September 3, made at 

Cadiz, By Augasto T. Arcimis. 

At 7^ I commenced the observations. The state of the atmo- 
sphere was magnificent, not a single cloud was visible above the 
horizon, nor was the slightest breeze perceptible, the sky having 
an extraordinary and exceptional purity. To the west were 
visible the last glimmers of the twilight. I made use of a 4-inch 
refractor (by Secretan of Paris), with an astronomical eyepiece, 
of the power of 92 diameters. To sketch the projection of the 
terrestrial shadow I employed a reduced map of the Moon of 
Beer and Miidler and some photographs of Mr. Warren De La 
Rue, which I kept constantly before me. 

The hours are according to Cadiz mean time ; the geo- 
graphical co-ordinates of my observatory are : 

Lat. N. = 36® 31' 52"-8; 

Long. "W. Greenwich ■= o"» 25™ i V-J. 

At 7** 15"* I saw the penumbra which concealed the Oceanus 
Procellarum, Mare Imbrium, Sinus ^stum, and 
Mous Carpathus. 

At 7** 40™ I could see with the naked eye that the light was 
scarce in the NE. quadrant (invert, vis.) and took 
a reddish tint. 

At 7** 50™ (hour of the first contact) the shadow reached the 
peak Cleostratus (although of the precise moment 
I am somewhat doubtful), and enlarged itself rapidly 
to Mons Harpathus and Sinus Proris. Five minutes 
later I could see with great facility the shadow with 
the naked eye. 

I then applied the spectroscope to the refractor, 
directing it to the crater Lavoisier; the common 
solar spectrum appeared as it was expected, but as 
the shadow advanced and the light became fainter, 
I detected some of the absorption lines on the red, 
produced by the Earth's atmosphere. 

At S^ 5™ the limits of the shadow are, to the east, 38° lat. N., 
craters Lavoisier, Mairan, Plato, Archytas, Mayer ; 
and ends to the west in 82° lat. N. 

I applied again the spectroscope, and in the 



Not. 1876. 1876, September 3, made at Cadiz. ' 13 

darkest part of the lunar disk the spectrum was 
Httle visible on account of want of Ugbt, bnt near 
the limits of the shadow I found the tellnric lines 
on the red, between D and F, and above all between 
F and C, where they became very nnmerons. 

At 8^ 20™ the limit of the shadow crossed the 28^ lat. N., on 
the east, craters Briggs, Diophantns, on the middle 
of Mare Imbrinm, crater Autolycas, Palus Nebnlamm, 
crat«r Burg, Lacns Mortis, crater Endymion, and 
ends to the west in 60° lat. N. 

At 8^* 32™ the shadow reaches the crater Aristarchns ; this was 
its highest point, on the NE. quadrant. 

At 8^ 41*^ the light appeared again upon this crater, and the 
shadow pursued its descending path. 

At 8** 50™ the shadow is bounded to the east by 34° lat. N., 
crater Euler, Mons Apenninus, Hoemus, crater 
Macrobius, the boreal edge of Mare Crisium, and 
finished to the west by 30° lat. N. 

At S"^ 57™ time of the middle of the eclipse, according to 
the Ephemeris, and the shadow begun to the 
east by 36° lat. N., craters Euler, Manilius, on the 
middle of Mare Vaporum, crater Vitruvius, and 
ends to the west by 22° lat. N. 

At 9** 6™ the limits were, to the east, 40° lat. N., craters 
Diophantus, Euler, Pytheas, Manilias, Palus Somnii, 
crater Picard in Mare Crisium, and ended to the 
west in 18° lat N. 

The neighbourhood of the boreal pole which 
was the darkest, had an orange colour, and the 
other parts of the shadow were of a livid white, 
similar to the light of Saturn, 

I made another analysis with the spectroscope ; 
some of the telluric lines on the violet had disap- 
peared, but those on the red remained very visible. 

At 9^ 24™ the shadow is bounded to the east by 56° lat. N., 
craters Cleostratus, Sharp, somewhat to the north 
of Archimedes, Palus Pntredinis, craters Menelaus, 
Jansen, Condorcet, and ends to the west in 1 2° lat. N. 

At 9^ 49™ the limits are, to the east, 66° lat. N., craters Pytha- 
goras, La Condamine, at half the distance of Har- 
pathus and Senopidus, on the middle of Mare 
Serenitatis, crater Proclus, Mare Crisium, crater 
Agamm, and ends to the west by 16° lat. N. 

At ID** 4™ the last contapt iook place, with the shadow very near 
Mare Humboldtianum by 53° lat. N. on the NO. 
quadrant. 

It seems to mo that I can point out a small 
difference in this last contact between the observa- 
tion and the Ephemeris ; those which I have made 
use of are published here under the title of Nautical 
Almanac, 



i 



14 JDr. BaU^ OhBervatiofM ofMiaiOT PlaneU with xxiviL x, 




a 






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O^ Ov O^ 00 o^ 



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vp y> 00 
b^ o^ ob 



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so 00 «b so in 

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. ^ « w « w W PO 

S3 \b «o so so \A ^A 
^ + + + + + + 



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m »*• t*. 



+ + + + 



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Mr, FinUby^ On a Formula in (he 



xxxvn. I, 



A Method of deducmg the Formula for correcting the computed 
Time of an observed OccuUation for Errors in the 

Elements ctdopted. 

By W. H. Einlaj, B.A., First Assistant, Cape Observatory. 

In BesseFs method of computing occnltations the positions of 
the Moon and observer are referred to three axes at right angles 
to one another throngh the centre of the Earth : of which the axis 
of z is directed to the star (R. A. =: a', Declination = 2'), the axis 
of a; to the point in the eqnator whose U.A. is 90^+ a', and the 
axis of y to the point in the declination-circle throngh the star 
whose distance from the eqnator is 90° + ^'. When the oconltation 
takes place the projection of the place of observation on the 

Slane of xy lies on the circumference of the projection of the 
[oon's disk. Let the figure represent the projection on the 




piano xy of the Moon*s disk at the time T, and let P be the pro- 
jection of a place at which the occultation is taking place. Let 
P' be an adjacent point in the plane : through P and P' draw 
lines parallel to the projected direction of motion of the Moon's 
centre at the time T, and draw PR touching the circle at P. 
Then if PP' be small, P'R is approximately the distance that the 
Moon*s projection must pass through before the point P' is on 
the circumference. Draw P' B parallel to the tangent at P, 
cutting CP produced in D. Let PP' = d, and the angle PP' 
makes with the axis of a; = 90® — Q. 

With Chauvenet's notation the angle PAa; = 90® — N, angle 
CPB = \p ; and the Moon's relative velocity in its projected path 
is M, — the unit of length being the cquatoreal i*adius of the Earth 
and of time one mean hour. 



Nov. 1876. OompuiaUon of OcouUaUons. 17 

Now, from the figure — 

FF cos DPP =- PD - BP COS BPD, 
thatia PF cos (BPF-BPD) = FKoos BPD; 
OP rf COB {N-Q-(i80°-4')} = FK COB (i8o«-4') ; 

... p.j^^ <^co8(N-a + if>) . 

coe ^ 

pro 
and the time of Moon's projection describing P'R = — . If P' 

be the projection of a point on the Earth's surface not £ar distanl* 
from P, the time at which the occaltation takes place at this 

second station will be approximately T + A paper on this 

n 

case by the Rev. T. Chevallier, B.D., will be found in Vol. A IX, of 

ihe Memoirs, Now consider the case in which the projection of 

the Moon's centre undergoes slight changes of position owing to 

dight changes in the elements. These changes may for con- 

yenience be attributed to the point P with opposite signs. A' 

slight change common to both Moon and star has scarcely auy 

effect, so we need only consider relative changes. 

(i.) If the rela^ve increase of R.A. of the Moon and 

star be A (a —a'), then, v denoting the Moon's parallax, 

the Moon's centre will be moved through an arc equal 

to — ^ — : — I X circular measure of i'', perpendicular to the 

plane zy ; therefore, in this case, PP' is equal to — ^^ 

and parallel to irO, that is Q = 90°. 

• P'R « A (a-af) con B sin (N + 4>) 

X cos ^ 

(ii.) Let A (3— 0') be the relative increase of declination. 
Here PP' is equal to ^^ and parallel toyO, that is Q = o. 

IT ' cos t|» ' 

(iii.) Let Ac be the increase of the Moon's radius. Then 
F is on the line APB, that is Q = N. 

.-. FR = PF= ^^^ ^ 



cos (180— i^) cos lf»* 

(iv.) Let Att be the increase in the Moon's parallax. Put 
OC = R and angle CO* = 90°—©: then from this change C 
moves towards O a distance AR. 

d 

Now R = —' where a is independent of tt. 

sm IT ^ 

B 



i8 ' Mr. Ghristie, On Effect of Wear in the xxxvn. i, 

AR a cob t sin t ^ - ,- ooe «• . 

B Bin' T a r 

.-. PF- -aE = ^^^!-^. A»,aiida-«. 

•ptn B cosy. Ay cos (N + t^) coa B-¥nn (N-n^) ain > 
X coeifr 

COST. At y 008 (N4-4')'f4r 8in(N + 4') 

■■ • J » 

T coeifr 

wHere x and y are the co-ordinates of the Moon's centre at the 
time T. 

Since these small changes are independent of one another, 
their combined effect will be equal to their snm. 

total correction to thel _ snm of the sevegal valnes of P*B , 
time T in seconds / ^ ***» 

where h is the number of seconds in the unit of time ; that is 
correction -« r [sin (N + ifr) cos 8. A (a— of) + cos (N + tf') A (d— f) 

MT cos ^ 

•I-T.Ajc— {f 8in(N-t'lfr)+y C08(N + lfr}}C06 t.At], 

which is the usual formula, omitting the terms depending on 
error of eccentricity of the meridian. 

1876, July. 



On the Effect of Wear in the Micrometer- Screws of the Chreenwich 
Traiisit-Circle. By W. H. M. Christie, Esq. 

It has been the practice of observers to examine carefully 
the accuracy of micrometer^crews on receiving them from the 
maker's hands ; but no one, so far as I am aware, has considered 
it necessary to make any observation afterwards, though the 
effect of wear, when observations are made frequently, soon be- 
comes sensible. Under these circumstances, it may be desirable 
to give an account of a case in which considerable errors have 
been caused by continued use during a period of more than 
twenty years. 

The wear in the micrometer-screws of the Greenwich Transit- 
Circle first showed itself by a discordance between the Zenith, 
points deduced from the Nadir observation and from Stars respec- 
tively ; though the cause was not suspected till the beginning of 
1875, when a change in the position of the division in the field of 
view of the micrometer-microscopes was found to be accompanied 
by a change in the discordance fi*om + o"7 to — o"*6. This discord- 
ance first became KcnFiblc in the year 1868; but the error intJie 



Not. 1876. Miorometer-ScrewB df Qreenwich Tromaii-Ovrele. 19 

screws, as will be seen presently, existed certainly before that time^' 
tliongb its effect on the Nadir observation was insensible so long 
as tiie observations were distributed over the whole range of the 
screws. This was the case np to 1868, after which the system 
was altered, the Nadir observation being from that time made 
with the circle-divisions at o'* approximately. When the 
change in the discordance occurred at the beginning of 1875, ^^ 
Tables of successive revolutions of the telescope-micrometer, and 
also of the microscope-micrometer-screws were tested by means 
of the collimator, and it was found that there was considerable 
inequality in the latter. To obtain the corrections applicable to 
the different parts of the screws, four supplementary microscopes 
(which had only been used occasionally for determining the 
division-errors of the circle) were mounted and read for compari- 
son with the six ordinary microscopes. These observations are 
printed in the Qreethwich Observations^ 1875. ^i^m 457 com- 
parisons thus made, the continuous curve shown in the diagram 
has been laid down, the means of the separate apparent correc- 
tions tabulated for every tenth of a revolution having been 
smoothed by taking the means for each adjacent pair, and then 
the means of these results again in the same way. The 
ordinates give the corrections to the circle-reading corresponding 
to the revolutions and tenths of Microscope A, indicated above, 
which has been taken for convenience of application. Its reading^ 
were throughout 0^13 less than the mean of the six micrometer- 
readings. 

In 1868 similar observations had been made, though with a 
different object in view, namely, to determine the promible value 
of the outstanding division-error of the circle. They are, 
however, equally available for testing the revolutions of the 
micrometer-screws, and from 289 comparisons thus made, the 
corrections applicable in 1868 have been found. These are 
represented by the dotted curve, formed in the same way as that 
for 1875, but with the origin shifted o^'o8 to the left, since 
Microscope A in 1868 read on the average 0^*05 less than the 
mean. The revolutions and tenths of Microscope A for the 
1868 curve are given below. Both carves are thus virtually 
referred to the mean of the micrometer-readings. It will be 
remarked that the two curves are generally similar, giving large 
positive corrections for the middle of the range ; but that the 
curve for 1868 falls above that for 1875, the corrections being on 
the whole positive. In fact, the mean of all the individual 
observations of discordance in 1868 is +o'''2o, whilst in 
1875 ^^ ^ +o'''09. As these quantities considerably exceed 
the probable error of the result, which would be about o"'o3, it 
is possible that some systematic error, such as a difference in tiic 
ontstfinding division-error for the parts of the circle used in 
finding the Zenith-point with the ordinary and supplementary 
microscopes respectively, may have affected all the observations. 

This, however, does not interfere with the comparison of the 

b2 



$o Mr. OkriMe^ On Bffeet of Wear m ike xxrm. i, 

two enrreiyM the ordinates may be supposed reduced thronghoat 
hy 4- o'^'so axid + o^'op in the two cases respectirely. There 
is another point of difference between the two cnnres, wtich 
depends on the adopted correction for mns, and has the effect of 
making the aads of symmetry fall somewhat to the left in the 
dotted ounre, which consequently lies above the other at o', and 
&lls below it at 5*^. Now the wear will take place on the part of 
the thread against which the spring presses the hollow screw of 
the micrometer slide, and the cross- wires will consequently be 
oarried f^her from the head, that is in the direction of increas- 
ing readings. Thus, for any given position of the cross-wires, 
the head will give too small a reading, and a positive correction 
will therefore be required, iMs correction being larger for the 
middle of the range of the screw, which is the part most 
frequently used. One effect of this will be to increase the run, if 
the error at the large reading (4^*9 approz.) be sreater, algebrai- 
cally, than that at the small reading (o' approz!), and the same 
will apply to the correction for runs if corrections be substituted 
for errors. Now the corrections increase (algebraically) from 
negative to small positive readings, and decrease from large 
positive readings onwards, and thus the correction for runs 
vrill be greater (algebraically) when the small reading is taken 
on the negative side of the zero than when it falls on the 
positive side. In the former case the corrections for error in the 
aorewa will be algebraically increased for small readings and 
decreased for large readings by application of the correction for 
mna ; and this effect is purely arbitrary, since we may choose 
any nart of the screw for sero. 

Making due allowance for this, and also for the difierence in 
the sums oir all the corrections for the two sets, the dotted curve 
must be lowered o''*4 approximately at o% and raised o"'2 at 5% 
proportional changes being made for intermediate readings. 
The agreement between the two curves will then be remarkably 
okM»« except for the portion between o*" and I^ at which point the 
1875 ourve rises very abruptly, indicating that considerable wear 
has taken place in that part since 1868. This appears to be fully 
acoountod for bv the circumstance that in that year the practice 
waa commencea of taking the Nadir observation with the circle- 
diriakm at o' approximately ; and, as the obeervation is regularly 
Bsade twice a day, there would bo a preponderance of some 
4,000 obiMTaikms at this part of the screw in the course of the 
«^t years elapaed since i$68. 

It would thus appear that by far the givater portion of the 
wtar IB tlie micxtHneter^K'n^ws has taken place in the seventeen 
yeaia precediiMt iS6^ and that^ exc^ in the part between o* and 
V« tlN» <tTC«a have not stensiMv changed since that date. On 
ceaftpariag the sevetml tenths o!' any one revohition, the ccvrec- 
f»HM Ibr "7« ^S« and *o wtmld appear to be aK>nt o '^ smaller 
(a^ekmrnQv) than the othersk bnt the diflktUtr of eliminating 
tW rifcrt «c the lareer corT>^etk>B$ is considexabkw and the 
ai« loo saall to W determined with cMtaintv. 



Not. 1876. Miorometer'Soraiti of Qreenmeh Tranrit-Oinle. «t 





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xa . Spedroscopic BesuUsfor Motions of Stars xxxvn. i, 

The corrections ihns found are considerable ; and it is to be 
remarked that they are of the nature of systematic errors, 
affecting all the observations of any one star, which wonld 
usually be observed in the same part of the field of view of the 
telescope, and therefore, for sevend years, with the circle-division 
about the same part of the range of the micrometer-screw. This 
points to the necessity for periodic examination of micrometer- 
screws, though the effect of wear will be sensibly eliminated if 
the action of the spring be in opposite directions for every pair 
of micrometers, the readings increasing towards the head for 
one micrometer, and from the head for the other of each pair. 

It may be proper to add, that the accuracy of the screws of 
the four supplementary microscopes has been tested indirectly by 
comparison with new screws applied to the six ordinary micro- 
scopes, as well as directly by observations on the collimator. 

Royal Observatori/t Greenwich, 
1876, Nov. 9. 



Spectroscopic Besvltsfor the Motions of Stars^ cmd of Venus in the 
Line of Sight, and for the Rotation of the Sttn and of JupUer, 
made at the Royal Observatory, Greenwich, IT.* 

{^Communicated by the Astronomer Royal,) 

The recent results for Star-motions have been obtained in the 
same manner as those given in the Monthly Notices for last May, and 
the general arrangement is unaltered. As, however, it has been 
suggested by P. Secchi that the results may possibly be dependent 
on the position of the spectroscope, the reading of the position- 
circle (or the position-angle of the slit) is here added. The slit lies 
north and south, and the deviation of the ray is towards the east 
when the reading is 0°. This is the most convenient position, and is 
that in which most of the observations have been made. In the 
earlier measures made in 1874 observations were taken in each of 
the four quadrants ; but, as the position of the spectroscope did not 
appear to affect the result, the practice was discontinued. All 
the observations since then are therefore strictly comparable in 
this respect, and all stars would be equally affected by any error 
depending on the position of the spectroscope. As a check on 
the absolute values, however, some measures of the lines in the 
spoctrum of the Moon and of Venvs have been made in different 
positions. Special care has been taken to observe the stars in 
pairs east and west as far as practicable, so that the Earth's 
motion might affect the several observations with different signs, 
and also that any error depending on the position of the instru- 
ment might be eliminated. 

The means have been taken for the whole series of observa- 
tions of each star, including those given in the Monthly Notices 

* The BeeulU for the Rotation of the Sun and of Jupiter will be giren in 
the December namber. — [£d.] 



Nov. 1876. and of Vemu eic.^ made at Qreenwich. II. 93 

for last May. Where no mean is set down, the lesnlt is to be 
considered as still uncertain. Sufficient observations have now 
been aocomalated to allow of a fair estimate of the probable 
error in different cases being made. This depends £Etr more on 
the character of the line observed than on the brightness of the 
star, being least for those stars which show well-defined lines, 
SQch as uie b group ; whilst for stars such as Altair, in which 
the F-line is very broad and nebulous, the uncertainty is so great 
ss to make the spectroscopic method quite inapplicable. It may 
he remarked, that the range to be expected in a group of 
observations is five or six times the probable error, so that with 
a probable error of 10 miles a second the extreme discordance 
between individual results might be expected to reach 50 or 60 
miles a second. P. Secchi would appear to have overlooked this 
consequence of the theory of errors of observation. The stars 
have been grouped together, according to the character of their 
spectra, for the determination of the probable errors in cases 
where there were less than eight observations. The probable 
errors of the results are appendeid with the sign + • 

The measures of the displacement of the lines in the 

rtrom of the Moon and Venus have been made to test both 
accuracy of the method of observation and the truth of 
Ddppler's principle. In the case of the Moon, the motion in 
the line of sight is insensible, and the result of the observations 
shows a very satisfactory agreement with this. The motion of 
Venus has been observed at both elongations, the comparison 
being made in some cases with the brignt lines of hydrogen or 
magnesium, in others with the sky spectrum. The observations 
at the western elongation were made in the forenoon. The 
calculated motions have been deduced from the daily change of 
the distance from the Earth, as given in the Nautical Almanac. It 
will be remarked, that the observed motion is rather larger than 
the calculated, both for the approach and recession ; this may be 
due in part to the disturbing efiect of the juxtaposition of two 
nearly ooincideut lines. The discordance, however, is small, and 
may well be a mere chance error in each case ; at any rate, as it 
has the same sign as the motion, it serves to show that there is 
no systematic error. Geneiall}', the direction of the displace- 
ment to be expected was not known to the observer at the time 
of making the observation. 

In measuring the Rotation of the Sun, the great point aimed 
at was to prevent the San*s heat from in any way affecting the 
position of the line observed, by expanding the slit unsymmetric- 
ally. Several precautions were adopted to guard against this, 
and with perfect success, as the measures show. In the first 
place, a tin screen, perforated with a small hole, 0*2 inch in 
diameter, was placed three inches in front. of the slit, from which 
it was separated by non-conducting material. When this had 

been applied, as well as a diaphragm, with a hole of — inch close 



24 SpectroBoopio BesuUsfor Maticne of Biars xcrriL i, 

to the slit, no perceptible rise of temperature in the slit conld 
be detected, a very small portion only being exposed to the Snn's 
rays. Further, the slit was always placed radially on the Sun's 
limb, so that the Snn's heat might affect the two sides equally ; 
and, lastly, the slit was placed aUemcUely on the east and west 
limbs, by nse of the slow-motion in B.A., and not by allowing 
the dinmal motion to carry the Snn's image across the slit. By 
this plan the change from one limb to the other was made so 
rapidly that no sensible disturbance could take place in the 
interval ; and, further, the observations were made in a con- 
tinuous series. One set of jneasures of the east and west limbs, 
and another of the north and south are given as specimens. 
The observations were made in the order of numeration. 
' The north and south limbs were compared in exactly the same 
manner as the east and west limbs, with the slit radial, as a 
check on the system of observation ; but no ffreat care was 
bestowed on the determination of the position-angle on the Sun's 
limb, which may be many degrees in error, as it was not easy to 
verify this point. The observations, however, suffice to snow 
that the precautions adopted have removed the sources of error 
to which results by former observers appear to have been ex- 
posed. Particular care was taken to avoid any bias from previous 
knowledge of the direction in which a displacement was to be 
expected, the limb under observation not being determined till 
after the bisection had been made. In the calculated motion 
there is some uncertainty, as it is doubtful how &r the period of 
rotation deduced from Sun-spots will apply to the chromosphere, 
to the rotation of which the observed displacement is due. There 
would appear to be no reason to suppose that it takes part in 
the genei^ drift depending on the latitude which has been re- 
marked in Sun-spots. 

Many attempts were made to measure the displacement of 
the F-line due to the rotation of Jupiter^ but for a long time they 
were frustrated by the prevalence of haze near the horizon, the 
planet having large southern declination. On one occasion, 
however, the spectrum was seen fairly well, and some measures 
obtained which give a result in remarkable agreement with the 
calculated value. It is to be remarked, that the method can be 
applied to Jupiter with peculiar advantage, as the equatoreal 
velocity is veiy large, and its effect doubled by reflexion. Thus 
the observed displacement corresponds nearly to four times the 
equatoreal velocity. 

The velocity of light has been taken as 185,000 miles a second, 
and the distance of the Sun as 91,260,000 miles. 

Royal Ohtervatory, Oreemwieh, 
1876, Nov, 10. 



Not.l»76. imi<^7aw«6fc.,ifiaitoa<0r6ameA*-ir. ^S 



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24 8pectra$eopio BesuUsfor McfUona of Starrs xcrriL t, 

to the slit, no perceptible rise of temperature in the slit conld 
be detected, a very small portion only being exposed to the Sun's 
rays. Farther, the slit was always placed radially on the Sun's 
limb, so that the Snn's heat might a^ect the two sides equally ; 
and, lastly, the slit was placed alternately on the east and west 
limbs, by use of the slow-motion in B.A., and not by allowing 
the diurnal motion to carry the Sun's image across the slit. "Bj 
this plan the change from one limb to the other was made so 
rapialy that no sensible disturbance could take place in the 
interval ; and, further,' the observations were made in a con- 
tinuous series. One set of measures of the east and west limbs, 
and another of the north and south are given as specimens. 
The observations were made in the order of numeration. 
The north and south limbs were compared in exactly the same 
manner as the east and west limbs, with the slit radial, as a 
check on the system of observation ; but no ffreat care was 
bestowed on the determination of the position-angle on the Sun's 
limb, which may be many degrees in error, as it was not easy to 
verify this point. The observations, however, suffice to snow 
that the precautions adopted have removed the sources of error 
to which results by former observers appear to have been ex- 
posed. Particular care was taken to avoid any bias from previous 
knowledge of the direction in which a displacement was to be 
expected, the limb under observation not being determined till 
after the bisection had been made. In the calculated motion 
there is some uncertainty, as it is doubtful how &r the period of 
rotation deduced from Sun-spots will apply to the chromosphere, 
to the rotation of which the observed displacement is due. There 
would appear to be no reason to suppose that it takes part in 
the general drift depending on the latitude which has been re- 
marked in Sun-spots. 

Many attempts were made to measure the displacement of 
the F-line due to the rotation of Jupiter^ but for a long time they 
were frustrated by the prevalence of haze near the horizon, the 
planet having large southern declination. On one occasion, 
however, the spectrum was seen fairly well, and some measures 
obtaineil which give a result in remarkable agreement with the 
calculated value. It is to be remarked, that Uie method can be 
applied to Jnpiter with peculiar advantage, as the equatoreal 
velocity is veiy large, and its effect doubled by reflexion. Thus 
the obeerred displacement corresponds nearly to four times the 

The Telocity of Hght has been taken as 185,000 miles a second, 
and tiie distance of the Sun as 91,260,000 miles. 

1876^ JiMt. la 



Kor. 1876. iwmZ <2f Yemu ek,f made id Qretmrick. U. 95 



ti 



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36 



^teotnteopie B e$ mUi for IMiona tf fitort . xxxvn. s, 







:» 

& 













I I I I 



« *^ »«* *n 

s a a i? 

ill! 



*« M M 
+ + + + 



r» 1^ o 






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to r* 

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M M 

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Not. 1876. tmd e^ YmM ete,, made at Onemeiek. U. 



»7 



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tN, 


M (^ 


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38 



8peetro$eop%6 BetuUsfor Motions o/Bian zxxvu. i, 




i 




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to %p 

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+ + + + 



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to to 



to 

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to ct 00 f^ p\ 

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rO ^ »« M MM 

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a 



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to 



a a 



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Nov. 1876. and of Vemu eic,^ made ai Oreenwieh. II. 



«9 



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d 



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mm* 

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o 
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B 

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s 









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+ + 



+ + 



ro SO 
+ + 



;^ F^ 



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O 
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+ 



OS 
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6 



broad 
edges, 




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to 11 





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30 



8pectro9cop%c BesuUs for Motwfis of Bkun xxxyil i 



a 





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« to « ►^ w 

I i 1 1 I I 



M ^ t^ \0 N tr> 

• . • • •_ • • 

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r^ ro M M M 

I t I I I 1 



ft 

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lo m ^ ^ ro M 

1 I I I I ( 



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b\ 00 

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Vo7. 1876. and of Venu9 etc.^ made at Oremnwich, U, 31 









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32 SpeGiroacapic BesuUafor Motdona of 8ia/n xzzvii« i, 





So 



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a9 



a 






?? -S -e So .S s •« -3 

^ ^i A A ^ 1 1 i 



o p o • o o o 

*''5 ^ « a a P d 

lU I i I i i 



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fo ^ o o »'> 

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+ + + II 



O^ 00 

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i^N "(f 0^0\000Q 

to'-' '^ WWtOrOfOrO 

I g ^ < i 

yO NO ^0 

»^ *^ ^ 

00 00 00 



Not. 1876. and 0/ Venus etc., made at Qreomnkh. IL 



33 



I 



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a 

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b \b 



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o 



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: »*> *o « CO ^ ^ ^ 

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• • • • ,'• • •_ 

^ I I 1 1 1 I t 



PqPx4FiHtX4Pq^^<r 



tn^O^O OSOO ** r<*^ 



o o o o o o : : 



JO ox 



M N N M 



N M rO ro 



wmNnww'mm 



MN<^'-«CO'^<< 



'JMjaiqo 



P^ S J?; J53 J^ 






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34 



Bpeciroeeopie BetuUsfar MoUofiB of Stars xxxvii. i, 






S 
I 



a 

■i 



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s 

a 

a 



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a o 



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a 



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in *^ 

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to ^ ** 



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b\ «o fo w 

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\r% 



+ 



+ 



+ 



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+ + + 






a 
o 



<r ^ ^ Pm Fq Pm <r 



o 

CO 



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vo »n »/> wt^t^t^vO 

■ • • ••••• 

.qO O O mOOOO 



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00 
in 



op Op fO 
in in to 



1^ r^ »^ r>« 
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M C4 C4 MMMCIM 



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Nov. 1876. and of Venus etc,^ made at Qreenvrich. II, 35 






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5 

a ■ 14 



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a 

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a - 
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+ + + + + -I. + + 



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3 



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JO ox 






d 
1^ 



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5r^,<r<rpq p4 p4 pm 






ot^ 1^ t"^ t^ fO PO PO ^O 



o 



o 

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a 






a 



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h 00 



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+ + 



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vb NO o 

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+ + + 



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fO fo ** ** ** ►^ 

+ + + + -++ + 

d a 

dS o 

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■ ■ • • • * ^ g 

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p O p 00 CO op 

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36 Spectroscopic Results for Motions of Stars etc, xixvii. i, 






■3 



•a 

a 



6 




IS 






i! 






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'*^p!^7^^ pr^ooop p pt* f*^ r*?** 



•oooooo^oooooooqqQ 



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}<5 



Nov. 1876. Mr. Penrasef SvnipUficatwn of Method etc, 37 



An Endeawmr to simplify the Method of making the Correction for 
the Spheroidal Figure of the Earth in Lunar Observations, 
and particularly with reference to its effect upon the *' Lunar 
Distance" By F. C. Penrose, Esq. 

The correction for the Spheroidal Figure of the Earth is 
generally neglected in ordinary Lunar Ohservations. Nor is 
this to be wondered at, if the navigator is expected to follow the 
roles generally laid down for the purpose. 

In endeavouring to simplify these rules, I lighted npon a plan 
which cleared up these difficulties to a very great degree ; but, 
as it has been since pointed out to me, the discovery has been 
anticipated and its value already recognized. 

This, however, does not, I think, preclude my bringing it 
before such members of the Socieiy as are unaware of it, espe- 
cially as it does not appear in the works mostly in use ; and I 
indulge in the hope, with the help of a graphic process, to render 
the management of this correction so easy, that there can be no 
reason for its being any longer neglected. 

The quantity involved is sometimes so large as to be out of 
all proportion greater than the smaller corrections which are 
often scrupulously attended to : such as great accuracy in inter- 
polating between the arguments of parallax, or in allowance for 
EMkrometer and thermometer under ordinary conditions. 

[I am not advising the neglect of these corrections ; but only 
that when time is an object, mey may be followed up somewhat 
more roughly ; so that the time saved in them may be used for 
the correction for the Spheroid.] 




When the Moon is referred to the Earth's centre C by the 
polar distance (viz. : through PCM and the radius vector CM), 
for any point Z at any latitude, its parallax must be reckoned 
from the line ZC, which does not agree with the plumb-line — 



38 Mr. PenrotB, Simpl^ieation ofMethoi ofmaldng xxxm. i, 

the standard of onr measaring instramenta — which intersecfai 
with the polar axis at sumo point N beyond the centre. 

By referring the observation to the point X, the complication 
of having the astronomical senith and the geocentric zenith to 
deal with, which tronbles all azimuths except the meridian, is 
avoided. 

This only reqaires that the value of CN for amy latitnde 
ahonid be tabnlated (call thia valne n), and that an allowance 
should be made to the declination given in the Nautical Almanac, 
^ n cos D ; if D be Moon's declination (geocentric). 

This correction is always to be subtracted from the polar dis< 
tance. Bnt inasmuch as in this reckoning, the radius measuring 
the Moon's horizontal pamllai for the latitude in question is NZ, 
instead of C Z, the tabnlar H P will have to be varied accordingly. 

If, therefore, to the table above referred to are added the 
values of N Z, as well as thoae of n, the correction can be made 
by inspection. 

These tables are given below. 

If these corrections are first made in the original elements of 
computation of any lunar observation, the purpose is answered. 

If, for instance, an altazimuth of D has been observed, and 
these corrections be given to the element* of declination and 
parallax (there is no trouble with the aztmiiths), the Moon's hour- 
angle will at once be obtained. 

But in many cases it may answer better to add this spheroidal 
effect as a correction afterwards, and for that purpose I have pre- 
pared a specimen-diagram adapt«d to latitude 50° (of oourBei 
North or South as the case may be). 




Suppose the question to be the cfiuct npon the altitude when 



Lntitudn 50 
lleclinutjon zo 
AllitudH 40 



P.Lr..llax ST- 



These give an hour-anglo of about 51°. 



Not. 1876. Correction for Spheroidal Figvre of Earth, 39 

The ordinate in the diagram corresponding to these places 
chows 1 3"* 4, hut when reduced for declination by applying it 
to the slant line, it gives I2'''4, the answer required. 

The hour-angles figured o, 10, 20, 50, 90 repeat after 90° ; 
for instance, the value corresponding to 130° is the same as that 
of 50**, etc. 

Grenerally, the correction must he added to the altitude ; hut, 
if Moon's declination is greater than the latitude, the sign must 
be reversed, and it must be subtracted. 

Probably the most important view of this correction is its 
bearing on the Lunar Distance. 

This can be readily measured upon similar diagrams, if what 
has been called Latitude be taken for the star's altitude. 

I have put together a case, which can be worked upon the 
diagram given : — 

o 

Lot the Latitude be 50 

Moon*s Declination 20 

Apparent Altitude 30 

Distance 30 

These values require Moon's hour-angle about 66° 30', and 
the azimuth-angle with respect to the star, 30°. 

Treat the first on the diagram with hour-angle 66° 30', alti- 
tude 30°. The ordinate on the chart gives 13", but applied to 
the declination line, I2'''4. 

Now consider the star's altitude as 50°, and the combined 
asimuth 30°. 

The ordinate reads "j6 on the division under hour-line o. 

Then 12*4 
76 

7" 

94 Answer. 9"*4. 

There are cases where 9"'4 in a lunar distance would in. 
finence the longitude by 45", and often this amount of 9'''4 
would be much exceeded. 

Similar diagrams can also be used for many other purposes : 
as for instance, approximately giving the corresponding azimuth 
to a given altitude and hour-angle and declination. 

They may also be used to form the entire operation of clear- 
ing the distance, instead of the small correction only above 
given, with a fair amount of accuracy. 

Clearing the distance by means of the diagram in the example 
above given, HP bcin^ 57', parallax in altitude affected by 
refraction = 50' 56". This worked out fully gives 49' 38" for 




40 Ifr. Pewrosey SimpUfication of Method etc. xxxvn. i. 

its effect npon the distance. Using the decimal fraction previ- 
ously found npon 50' 56", we obtain 49' 28". 

And even where exactness is required, an approximation 
easily obtained will enable the work to be shortened, in this 
manner, viz. : 

Let Z be the Zenith ; M the z^ 

Moon's apparent altitude ; M M' 
the Parallax in altitude = p. 

If M M' were very small, the / ^.J*' 

effect would be simply=jp cos M 

^ds' 

This will not, in ordinary 
cases, be sensibly incorrect if the 
point Q half-way between M and 
M' be taken, and a proper allowance be made for the alteration 

of SM. The altitude of Q comes at once by applying ?. ; and 

2 

the corresponding value of S Q results from the approximation 

referred to derived from the diagram. 

In estimating these corrections, whether of the whole effect 
known as clearing the distance, or only the part resulting from 
the spheroidal figure, which is the particular object of this dis- 
cussion, it is of course of primary importance to know whether 
it should be estimated + or — . 

This will always depend upon the angle at the Moon ; calling 
this M, when M is greater than 90^, the distance will be in- 
creased, when less, diminished. When the star's altitude is 
greater than that of the Moon, the angle at M is always acute. 
Also, when the distance S M is greater than the star's co-altitude, 
M is always acute. 

Bule for doubtful cases : — M will be acute or obtuse, ac- 
cording as cos b is greater or less than cos z cos s. 

1876, Nov. 10. 



MONTHLY NOTICES 

OF THE 

ROYAL ASTRONOMICAL SOCIETY. 

Vol. XXXVII. Dbcbmbbr 8, 1876. No. 2. 

WiLLUM HuQGiNS, EsQ., F.R.S., President, in the Chair. 

Capt. James Waterhouse, Surveyor General's Office, 
Calcutta, 

was balloted for and dnlj elected a Fellow of the Society. 



Nate on Prof. Langley^a Paper on the Direct Effect of Suri'spota on 
Terrestrial GUnuUes. By W. Mattiea Williams, Esq. 

Prof. Langley determines quantitatively the effects respectively 
produced by the radiations from the solar spots, penumbra, and 
photosphere upon the face of a thermopile, and infers that these 
effects measure their relative influence on terrestrial climate. 

In thus assuming that the heat communicated to the thermo- 
pile measures the solar contribution to terrestrial climate, Prof. 
•Langley omits an important factor, viz. the amount of heat 
absorbed in traversing the Earth's atmosphere ; and in measuring 
the relative efficiency of the spots, penumbra, and photosphere, he 
has not taken into account the variations of diathermancy of the 
intervening atmospheric matter, which are due to the variations 
in the source of heat. 

Speaking generally, it may be affirmed that the radiations 
of obscure heat are more largely absorbed by the gases and 
vafMurs of our atmosphere than those of luminous heat, and the 
great differences in the mere luminosity of the spots, penumbra, 
and photosphere justify the assumption that the radiations of a 
ftan-spot will (to use the expressive simile of Tyndall) lose far 
more by atmospheric sifting than will those from the photo- 
sphere. 

But the spot areas will be none the less effective on terrestrial 
climate on that account. A given amount of heat arrested by 
the Earth's atmosphere will have even greater climatic efficiency 
than if received upon its solid surface, inasmuch as the gases are 
worse radiators than the rocks, and will therefore, cnderU paribus^ 
retain a larger proportion of the heat they receive. 

D 



42 Mr, Williams^ On Prof, Langley*8 Paper etc. xxxYn. 2, 

I have long ago endeavoured to show* that the depth of the 
photosphere, ^m the solar surface inwards, is limited bj dis- 
sociation ; that the materials of the Son within the photosphere 
exist in a dissociated, elementary condition ; that at the photo- 
sphere they are, for the most part, combined. This view has 
since been adopted by many eminent solar physicists, and if 
correct, demands a much higher temperature within the depths 
revealed by that withdrawal of the photospheric veil which 
constitutes a sun-spot. 

If I am right in this, and also in supposing the spot-radiations 
to be so much more abundantly absorbed than those of the 
photosphere, that in spite of the higher temperature of the spots, 
the surface of the earth receives from them the lower degree of 
heat measured by Prof. Langley, another interesting consequence 
must follow. The excess of spot-heat directly absorbed by the 
atmosphere, and mainly by the water dissolved or suspended in 
its upper regions, must be especially effective in dissipating 
clouds and checking or modifying their formation. The meteoro- 
logical results of this may be important, and are worthy of 
careful study. 

In thus venturing to question some of Prof. Langley's 
inferences I am far from underrating the interest and importance 
of his researches. On the contrary, I regard the quantitative 
results he has obtained as especially valuable and opportune, in 
affording means of testing the above-named and other specula- 
tions in solar physics. Similar observations repeated at different 
elevations would decide, so far as the lower regions of our 
atmosphere are concerned, whether or not there is any difference 
in the quantity of heat imparted by the bright and obscure 
portions of the Sun to our atmosphere. If the differences already 
observed by Prof. Langley vary in ascending, a new means will 
be afforded of studying the constitution of the interior of the 
Sun and its relations to the photosphere. Direct evidence of se- 
lective absorption by our atmosphere may thus be obtained, which 
would go far towards solving one of the crucial solar problems, viz. 
whether the darker regions are hotter or cooler than the photo- 
sphere. 

The obscure radiations from the Moon must be absorbed by 
our atmosphere like those from the sun- spot, and may be suf- 
ficently effective to account for the alleged dissipation of clouds 
by the full moon. 

In both cases the climatic influence is greatly heightened by 
the fact, that all the heat thus absorbed is directly effective in 
raising the temperature of the air. The action of the absorbed 
heat in reference to cloud -formation is directly opposite to that 
of the transmitted solar heat, which by evaporation of surface 
water supplies additional cloud material, instead of effecting its 
dissolution. 

♦ TTie Fuel of the Sun, chapters 4 to 10. 



Dec. 1876. Spectroscopic Renulinfor Botation ofJupUer ete. 43 






I 

o 



^ 1 

5 ^ 



'2 ** 

- IS 

3 

IS 



1^ 



:§ 















•s. 



2i 

ft; 



I 



(>> 
00 

& 

I 

-«: 
^, 

CO 

5s 



ft 



« 

J3 



O 

s 

"El 

80 



o 
« 

•5 

I. 

to o 

•5 s 

O «Q 

a 9i 






5 — 

ft* « 



J3 ;:3 
a 9 
H 



JB 






J 

o 
6 






SO 








-J 

fl OQ 

> a 



i 






J 



■3 •'S 



I 
8 

1 

M 
fO 

4 

I 

a 

► 

I 



U H ►^ 




■ 

Q 



M O 

+ + 




P 

+ 



» 



Pn ;*4 P«< 



•uonisoj 



•o 6 



o^ 



o ^ 



NO NO 



JO -ox 



«« 






*K)Lin8uajf 

JO'OM 

*j Ajasqo 



» 1^ s 





^ 


NO 


NO 




M 


N 


<t 











3 

eg 


fl 







;::) 


•-a 







NO 

QO 



P 2 



44 Spectroarnpic Results for Rotation of the Sun, XXXYII. 2, 



Rotation of the Sun. 

Dispersion — Ten Compound Prisms ; Magnifying Power 36. 
!'•▼• of Micrometer = 33 tenth-mitres, corresponding to 103 miles per second at D 

= 20 „ „ 72 „ „ b 

The readings increase towards the blue. 
1876, May 30* 4^ Observer— IVIr. Cliristie. 

Measures of the lino 5161*5 (Angstrom) near b^ 

Micrometer Readings. 

Position-Circle 270**. 
K. Limb. W. Limb. 



(0 -379 

(3) -374 

(5) 372 

(8) -400 

(10) 402 

(12) -372 

(14) 378 



(2) -335 

(4) 346 

(6) -362 

(7) -366 
(9) -363 

(") -342 

('3) -358 



Displacement. 
E. Limb— W. Limb. 

r 


+ (ro44 


+ 0028 


+ 0010 


•f 0034 


+ 0-039 


+ 0-030 


+ 0040 



Mean displacement, E. limb — "W. limb +0*032 

corresponding to 4 2*30 miles per second 



Porttion-Circle o°. 



S.I 

(0 


^imb. 
•634 


N. ] 
(2) 


Limb. 
r 
•649 


S. Liml>-N. Limb. 

r 

—0015 


(3) 


•645 


(4) 


•635 


+ 0010 


(5) 


•610 


(6) 


•613 


— 0-003 


(7) 


•-628 


(8) 


•621 


+ 0007 


(9) 


•646 


(10) 


•639 


+ 0007 



Mean displacement, S. limb— N. limb +0*001 

corresponding to + 0*07 mile per second 
Probable error of i measure of dispbicement =o'"*oio or 0*7 mile per second 



Concluded Motion in miles per second. 





roBition- 
Circte. 


Lino 


No. 
of Ob8. 


E. IJmb--W. 
ObPcrvwL 


1876 May 29 



90 


I), 


20 


+ 2 26iO-l6 


30 


270 


D, 


7 


+ 226 ± 0-27 


30 


270 


near h^ 


7 


'^- 230 ±0*27 


30 





D, 


6 


S. Limb-N. Limb. 
+ 0*02 ± 0-29 


30 





near h^ 


5 


+ 0*07 ±0-3 1 



Calculated. 



+ 235 



The part of the spectrum observed was in each case at a distance of alx>ut 
8" from the limb. 

The position-angle of the Sun's N. Pole was 344j°. 
The period of rotation has been taken as 2$ J days. 



Uec. 1876. Mr. Sione^ On Phenomena oj Internal Ocniar.ts etc. 45 



On the Error of the Tahidar Place of Venus on December 8, 1874. 
By Colonel J. F. Tennant, R.E., F.R.S. 

{From a Letter to E, Dunkin, Esq,, F,R.8,) 

After coming here last January I compared the tabular places 
which I got for the transit of Venous by the Astronomer BoyaPs 
tables with those I had used. I found that the printed tables were 
2^*03 in excess of mine in the B.A. of the Sun. I was anxious 
to find the source of this before saying anything about it, but 
many interruptions have occurred. All I can say is, that making 
a third computation in the same way that Captain Campbell and 
I had deduced all the formulas, I got results only numerically 
different in the last place from those I had got oefore. It is, 
nevertheless, a fact that the Tables published at Greenwich are 
right ; but it is curious that Captain Campbell and I, using an 
arithmometer in computations, should have entirely agreed, and 
that a third calculation with a different instrument gave the same 
result, all three being wrong. 

Now to the effects. In the Monthly Notices of November 1 87 5, 
you gave errors of the place of Venus. These are affected in 
K.A., and I have already sent you a correction to the difference 
in N.P.D. With the new correction they should stand : — 

Correctiou to (R.A. ? ) -(B.A. 0)= + 6"-5o-o"o7i ^L-o-qSq rf», 
(N.PJ). 9 )-(N.P.D. 0)= -2''-24-o"-oi7 <iL-2-689 <ftr. 

Calcutta, 

1876, November 3. 



On some Phenomena of the Internal Contacts common to the Transits 
of Ventts, observed in 1769 and 1874, and some Remarks 
thereon. By E. J. Stone, M.A., F.B.S., Her Majesty's 
Astronomer, Cape of Good Hope. 

When the Observations of the Ti-ansit of VentLs, 1874, are 
published in detail, I hope to examine the observations of the 
internal contacts with reference to their bearing on our deter- 
minations of the Sun's distance. I should have preferred not to 
have written upon the subject before the whole of the materials 
collected were available. But an impression has been slowly 
hardened into a conviction that none of the skilled observers, 
who, in 1874, observed the internal contacts with good instru- 
ments, saw the so-called black-drop phenomenon. Such an 
impression is, I am quite sure, unfounded, and it is perhaps 
desirable that this should bo pointed out. T\\v cssentiiil facts 



46 Mr. Stone^ On Phenomefia of Internal CotUacU xxxTii. a, 

are in this case, as in too many other cases of the kind, becoming 
veiled in a mist of words. 

Undoubtedly, if we are prepared to assume, on a priori 
grounds, that what a good observer, provided with a good instru- 
ment, should see, is the simple geometrical contact at a point, 
and iJiat any observer who has seen more, must be either an un- 
skilled observer, or have been provided with a defective instru- 
ment, we shall find no difficulty in establishing, to our own 
satisfaction, the conclusion which I have mentioned. But, on 
the other hand, there will be no difficulty in showing that 
observers have seen the *' black-drop," who would have been 
considered observers of skill, and to have been provided with 
good instruments, had their observations not failed to satisihr 
some preoonceived ideas of the nature of the phenomena whicn 
should be presented at the internal contacts. And here, perhaps, 
I may be permitted to add a word or two in the way of a caution. 
Notmng whatever depends upon the phrase " black-drop " or 
'* black-drop phenomenon." This is merely the way in which one 
observer, in 1769, thought proper to aescribe the lingering 
nature of the contact, which is the cause of the only systematio 
error to be feared in a discussion of durations derived from in- 
ternal contacts, and the cause of the principal systematic error 
in a general discussion of contact observations. 

Whether the observer prefers to speak of the disturbance of 
the apparent limb of the Sun near the point of contact, as an 
" ombre," a " black-drop," a " ligament," a " thread," or merely 
to assert generally, that " the contact was gradually established," 
is a point of very little importance. 

The important point connected with these protracted con- 
tacts is the sensible time over which the contact extends ; this 
renders no longer admissible the assumption that all contacts 
take place with the same angular separation of the centres of 
Venus and the Sun. For if, at ingress for example, after the 
geometrical contact appeared to be established there still con- 
tinued for thirty or more seconds some disturbance of the Sun's 
apparent limb, near the point of contact ; the time at which the 
observer saw the geometrical contact, and the time at which he 
last saw any disturbance of the Sun's limb near the point of con- 
tact, cannot be combined toother in any mathematics investiga- 
tion without allowing for the relative change in the positions of 
Venus and the Sun in the thirty or more seconds which elapsed be- 
tween the observations, or without accepting residual errors of 
fifteen or more seconds. And when we have to combine observations 
of contacts made by different observers, we cannot proceed a single 
step without an assumption. We have to assume that contacts 
of apparently the same class take place at all the different stations 
with the same angular separations of the centres. Unless this 
assumption is approximately true for some class of contacts, 
attempts to determine a value of the solar parallax from contact 
observations in a transit of Venvs must entirely fail. It is, how- 



Deo. ibyb. common to the Transits of 1769 and 1874. 47 

erer, a pore assnmption, which may or maj not turn ont to be 
correct. Like other assumptions of the class, it can only be 
proved or disproved by logically tracing its conseqaences, and 
comparing them with the known facts, which are the observations 
made at the different stations. 

Bnt suppose, as will be found to be the case, that some of the 
observers, who have seen the contact of a lingering or protracted 
character, have preferred to give as the time of contact the times 
when they saw the so-called geometrical contact, whilst others 
have preferred to give the times at which* at ingress they last 
saw, or at egress first saw, any disturbance of the Son's apparent 
limb near &e point of contact. How are these incongruous 
observations to be combined P It is clearly useless to attempt 
to combine them under a single assumption, that all the contacts 
took place at the same augnlar separation of the centres of the 
planets, unless we are prepared to admit, in the comparison of 
our theory with the observations, residual errors, or so-called 
errors of observation, at least equal to one-half the time over 
which the contacts have been observed to be prolong^. Enough 
IB already known of the observations made in 1874 to justify the 
statement that these contact observations thus treated cannot 
lead to any accurate value of the solar parallax without the 
adoption of some method of selection of materials equivalent to 
the rejection of a considerable number of observations.' If we 
were sufficiently acquainted with the causes which produce the 
appearances of prolonged contact, and were in possession of the 
requisite data upon which to base the necessary calculations, our 
proper course, to utilise the whole of the contacts, would be to 
adopt as our standard phase the real contact, an expression which 
in the case supposed would have a clear, distinct, and definite 
meauing, and to apply corrections to the times of the observed 
contacts to reduce Uiem to the corresponding times of real con- 
tact. Bnt an error of a tenth of a second of arc in assumed 
difference of semi-diameter is equivalent to an error of three 
seconds in time in the observed contact. I am afraid that we 
possess neither the theoretical knowledge nor the requisite data 
to render such a method available within allowable limits of 
error. If such be the case, we are thrown back upon the method 
which I adopted in my paper on the '^ Bediscussion of the 
Transit of Venus^ 1 769." Just as we assume that all the observa- 
tions of g^eometrical or apparent contact are seen at some definite 
aogalar separation of the centres of the planets, so must we 
assume that all the observations of the first Bknd last disturbance 
of tho Sun's limb near the point of contact take place at a 
definite angrular separation of the centres. The second assump- 
tion is as legitimate as the first; its approximate truth can only 
be proved or disproved in the same way, by loj^cally tracing the 
consequences of the assumption and comparing them with the 
observations. In practice we must expect to find both of these 
iptions satisfied with greater or less accuracy, according as 



48 Mr. Stone, On Piveywniena of Internal Coniacts xxxvil. 2, 

greater or less nnifonnity has been secured in the instrumental 
equipment of the observers, the brightness of the field of yiew 
in which the observations were made, and in points to which the 
attention of observers was specially directed. 

In the transit of 1 769 there were ten complete observations 
of duration from internal contacts. The smallness of the 
residual errors in my rediscussion of these observations proves 
that, so far as they are concerned, the assumptions to which I 
have called attention were at least very approximately satisfied. 
Whether such will be the case with the contact obs^vations of 
1874 remains to be seen. The similarity of the phenomena of 
the contacts observed in 1769 and 1874, to which I shall call 
attention, may probably have some effect in reassuring astronomars 
of the objective character of the phenomena, and may thus render 
more general the acceptance, as at least d priori probable, which 
is all that is required, of the assumptions which I have already 
mentioned and of the other supplementary assumptions of the 
same class, which the want of uniformity m instrumental equip- 
ment and attempts to introduce subsidiary phases, which appears 
to have been made in 1874, may be found to have rendered 
necessary. 

I have entered into these details because they must be 
understood before the importance of the remarks made by the 
observers can be appreciated, and because the principle upon 
which my " Rediscussion of the Transit of Venvs, 1 769," is baised 
has been entirely misunderstood by one popular writer on the 
subject. 

In the present paper I shall make no further reference to my 
own observations than to say, that I saw the so-called penumbra 
of Cook and Green. The light of the penumbra was, however, 
so faint in comparison with the direct light of the Sun that, when 
attention was concentrated on the contact all distinction between 
the central darker portions of the planet were lost sight of. The 
disturbance of the Sun*s limb at egress appeared to me to conu 
mence some considerable time bSore the apparent contact, 
when, in fact, the limb of Venus was more than the second of 
arc from the apparent limb of the Sun. At first, however, the 
disturbance was of a very slight character. The appearance at 
first presented was something like that of a hair in vibration 
before the eyes. Such an appearance I consider as an indication 
that some of the pencils of light which had previously reached 
the eye from the Sun's disk were more or less interrupted by the 
planet Venus or its atmosphere. The appearance of disturbanoes 
soon assumed a definite character ; and I should be content to 
describe the connection between the limbs of Venus and the Sun 
as a ligament. The apparent contadt was rendered more difi&oult 
than would otherwise have been the case by the appearance of this 
ligament, or, in other words, by the disappearance of a sensible 
portion of the Sun's limb near the point of contact. The obser- 
vations of Contiict were made in a rather bright field of view. 



Dec. 1876. common to the Trarufiis of 1769 and 1874. 49 

The definition was good, the sky perfectly free from clonds, and 
there was bat little wind. 

I am aware that it has been stated that my observations have 
been affected by my theoretical views ; and, as the same charge 
might probably be brought against some other observations to 
which 1 could appeal, I shall, for my present purpose, confine 
myself to observations made by the French observers. The 
instmmental equipment of these observers was supposed, before 
the transit, to be sufficiently perfect to prevent any instrumental 
defects affecting their observations. It is clear, also, that the 
observers, if biassed at all, were not biassed in fiivour of any 
Tiews of mine, and their observations have been printed in 
some detail, and are available for general examination. The 
observations to which I shall first appeal to prove that the 
phenomenon of the black-drop did pi-esent itself in the transit 
of 1874 are those made by M. Janssen at Nagasaki. M. 
Janssen, in describing the contact at ingress in the Annuaire^ 
1876, says that **lo premier contact est obtenu par M. Tisseraud 
et par moi. Dans I'equatorial de 8 ponces, dont la lanette est 
tres-bonne, Timage de Venus se montre tres-rondu, bien terminee, 
et la marche relative dn disque de la planete, par rapport an 
disqne solaire, s'execnta g^ometriqnement sans aucune apparence 
de ligament ni de gontte." Nothing can apparently be clearer 
than the statement of M. Janssen ; and it has therefore been 
seized upon as conclusive evidence against the black-drop in 
1874. But M. Janssen continues his account of his observations 
as follows: — "Mais il s*econla un temps assez long entre le 
moment ou le disque de Venus paraissait tangent interieurement 
an disque du Soleil et celui de Tapparition du filet lumineux." 
This prolongation of the disturbance of the Sun's limb near the 
point of contact after the geometrical contact, for a " temps 
assez long " constitutes what other observers have called, and I 
should call, the black-drop. M. Janssen has apparently con- 
fincxi himself to giving the time at which he saw the geometrical 
contact ; but he might, had he pleased, have given us instead the 
time later by the " temps assez long " which corresponded to the 
first appearance of the " filet lumineux." To show that this is 
really the point upon which controversy has hinged, I will give, 
for comparison with Janssen' s Observations, those made by Wales 
and Dymond in 1769. 

These observers state, "We took for the instant of last 
internal contact the time when the least visible thread of light 
appeared behind the subsequent limb of Vefiius ; but before that 
tune Venus' 8 limb seemed within that of the Sun." It is clear, 
therefore, that Wales and Dymond in 1769 and Janssen in 1874 
saw similar phenomena ; but that Wales and Dymond preferred 
to give the time corresponding to the last appearance of any 
disturbance, or to the first appearance of the " filet lumineux " ; 
whilst Janssen preferred to give the time corresponding to the 
geometrical contact. In the Annua ire for 1876 — where are also 



50 Mr. Stone, On Phenomena of Internal Contacts xxxyn. 2, 

some very important remarks by M. Janssen which appear to 
prove, in the most conclasive manner, the objective character 
of the phenomenon — ^M. JanRsen mentions thai, after the geo- 
metrical contact, he proceeded to take photographs, and that 
these photographs showed that the connection between the limbs 
of Venus and the San had not ceased. 

At the eg^ress, M. Janssen's observations wonld appear to 
have been pidced ap throagh cloads, and the details are wanting. 

The evidence thus afforded by M. Janssen of the existence 
of the black-drop in 1874 is not only of the most conclusive 
character, bat it is above any saspicion of being the resolt of 
preconceived ideas. It wonld appear that the observer had some 
misconception of the real character of the black-drop, and his evi- 
dence in £Ekvoar of its existence is given qoite nnconscioasly. The 
important fact mentioned by M. Janssen, that after his observa- 
tions of the geometrical contact the photographs still showed that 
the connection between the limbs had not ceased, proves that the 
prolonged contact is not a mere optical delasion, " for photographs 
have no nerves," to whatever otner sonrces of error they may be 
liable. It may be remembered that soon after the transit gpreat 
stress was laid npon the sapposed fact that Capt. Abney had 
secared a photo^^ph of the contact, and that there was no 
appearance of any black-drop. It was, however, foand, on exa- 
mination, that the contact hsul not even commenced at the time 
the photograph was taken ; bat the impression made by the 
original statement, althoagh admitted to be erroneoas, has never, 
I fear, been removed. The contradictions of snch statements do 
not nsoally receive the same publicity, or attract the same atten« 
tion, as the original statements. 

The next observations to which I shall refer are those made 
by Capt. Monchez at the Island of St. Paul. Capt. Monchez's 
telescope had an apertnre of eight French inches. The following 
accoant of these observations is taken from the Annnaire, 1876 : 

Speaking of the internal contact at ingress, Capt. Moachez 
says : — " Les nnages devenaient de plus en pi as rares, le ciel 
plus transparent, les images d'ane tres-grande uettet^. Un qaart 
d'heore environ apr^s le premier contact, qaand la moiti6 de la 
planete etait encore hors da Soleil, j'aper9as subitement toat 
le disqoe entier de Venus dessin6 par nne pkle aar^ole, plas 
brillante dans le voisinage da Soleil qa'aa sornmet de la planete. 
Ponr bien constater qae je n'etais pas le joaet d'une illasion, 
je pris imm^diatement des mesares microm6triqaes da diam^tre 
de Venus, dans le sens de la ligne des centres et dans le sens 
perpendicalaire ; bien qae le premier de ces diametres fiit encore 
a moiti6 hors da Soleil, et limite exteriearement senlement par 
Taor^ole, j'obtins, a i seconde pres, exactement la mSme valear : 
c'^tait done bien le disqae entier tres-net de la planete qae 
j'apercevais. 

'* Cette apparition, anssi remarqaable qa'inattendne, pent 
sans doato 6tre attribaco en partie a ratmosphcro solairc rendae 



Deo. 1876. common to the Traneita of 1769 and 1874. 51 

Tiaible par oontrasie, en partie anssi par ratmosphere de VSnus, 
he dei 6iait devena si par & la suite de la tempSte et raor^ole 
etoifc si brillante, qu'on pent voir sur nos photographies des traces 
de oe caiieiix ph&omene. Le deaxieme contact &t observe dans 
de bonnes conditions vers 7*^ 30™ ; mais, an lien de voir Tapparence 
de la goatte noire, qui a poor effet de tenir les denx comes encore 
•epar^es apres le contact, j'ai vn le ph^nomene tout contraire : 
Tare Inminenx de Tanr^ole r^nnissait ces denx comes avant le 
oontaci. Nous nous iarouvions ^videmment dans des conditions 
ezoeptionnellement favorables sous le rapport de la puret6 de 
Taimoeph^ et de Texcellence de notre lunette." 

It is to be regretted that Capt. Mouchez has not stated more 
dearlj whether there was or was not any disturbance of the 
Son's limb after the contact. 

It should be noticed that the circa mstances under which the 
inreole first presented itself to Capt. Mouchez are exactly 
nmilar to those under which it first appeared to Wales and 
Djmond in 1 769. 

These observers state, " Soon after Venus was half immerged, 
& bright crescent or rim of light encompassed all that part of 
the circumference which was ofif the Sun, thereby rendering her 
whole periphery visible. This continued very bright until 
within a few minutes of the internal contact, and then vanished 
away gradually." Upon these points see the observations of 
M. Heraud, wnich will be subsequently given. The observa- 
tions of Capt. Mouchez are chiefly valuable, for my present 
purpose, for the light which they throw upon Cook and Green's 
obeervations in 1769. The aureole is nothing more than Cook 
and Green's penumbra. I shall have something more to say 
upon this point with respect to MM. Heraud and Bonifay*s 
observations. 

The following accounta of the observations of MM. Heraud 
and Bonifay at Saigon are extracted from the Oomjptes Bendus 
(25 Janvier 1875) : — 

" Observation de M, Heraud. 
*'Objectifde 160 millimetres: grossissement, 155. 

'* Entree. — A 21^ 1 7°^ la planete 6tant d^ja entree de plus de 
deux tiers, je remarque que la partie exterieure de son limbe est 
nettement indiquee par un filet lumineux pale, qui, reuni aux 
firanges de I'image interieure, dessine un rond parEsut. Ne 
m'attendant pas a ce ph^nomene, je ne puis noter I'instant precis 
de son apparition ; I'heure ci-dessus est donnee a i minute pres. 

^* L'^hancrure s'arrondit de plus en plus, je suis le rapproche- 
ment regulier des pointes brillsuites du croissant solaire ; a un 
moment donn6, ces pointes me paraissent immobiles. Je ne vois 
plus la petite aur^le exterieure, la partie noire de rechancrure 
me parait absolument ronde et tangente h la ligne Active qui 
fermerait le bord du Soleil. Jc donne un top et, perdant de 



52 Mr, Stone^ On PhenonieHa of IiUemal Gontaets XXXTIL 2» 

vne les franges, je crois an moment qae le contact s'est prodait 
ot qn'il est perturb^ par la gontte noire. Je regarde aveo 
attention, et 20 secondes pins tard je note I'apparition entre 
i'image noire et le fond da ciel d'ane luenr tres-p&le teintde de 
noir en son miliea ; cette laear, qoi arrive comme an transitioii 
entre robsoarit^ et la lamiere, s*agrandit et s'anime, et, en mdme 
temps, la petite tache noire devient pins petite. Je la signale 
comme formant nne sorte de pont obscnr entre le bord dee astres 
qa'olle laisse cepondant distincts ; elle disparait presqne aossitAt, 
ot le filet lammeax est d^pooille de tont troable, les franges 
reprennent lenr nettet^ antoar de la plan^te. Los phenomdnes 
de Tentr^e sont accomplis 

'* Sortie, — Les images sont moins calmes qae dans la mating, 
mais encore nettes; Timage de la planefce est tonjoars bien 
frang^e. 

** La plancte se rapprochant de pins en pins, je sais attentive- 
ment le tilet lamineax. Je signale snccessivement I'apparition 
d'an filet lamineax tres-faible, pais celle d'an filet lamineax 
presqne nal. Le filet tres-plLle est teint6 de noir oomme dans la 
matin6e, et ressemble k ce qa*il ^tait lors de son apparition k 
Tentr^e ; mais je n'ai pas reva le ligament pins net signals dans 
la premiere observation. Tonte apparence Inminease disparatt ; 
c'est VinslafU du corUaci ; la partie noire de Timage de Vhiue eel 
i nne distance appreciable da bord da Soleil ; pea d'instants 
apres, cette distance me pandt nnlle, et r^hancrare noire semUe 
tangento an bord da Soleil ; les comes da croissant s'^loignent, 
mais sans prendre tont de saite Tacait^ qai correspond k ane 
intersection g^om6triqae; je les signale comme 6tant an pea 
^monss^s, ot ce n*est qae trente-trois secondes pi as tard qae 
rechancrare me parait bien nette. 

" Ohservatio7i de M. Bonifaij, 

'* La lunette dent je me suis servi est do la maison 
Secretan ; elle a an objectif de 55 millimetres d*oavertare et on 
grossisdoment de 63. 

*' 1a\ miso au point sar les etoiles et sar les taches da Soleil 
s*oiH>niit sans difficalt^^ et donnait des images tre-nettes. C'est 
cette mise an point qui ^to adoptee pour Tobservation. 

*' J'ai pa apres Tobservation, determiner, avec la lanette 
mi^ridienne nrise comme collimatenr, la mise au point sar le 
plan focal. EUe exigeait que le tabe de I'ocalaire fiit legerement 
moins enfonce qae la mise au point sur le oerde maxima m 
d'aberration. 

** L'observation a t^tc^ faite dans le Jardin de TObservatoire, 
avec cet<te lanette, montee en altasimnt, sar ane table massive, 
i 20 metres a Test do rObservntoire. 

** i?M/f>v>. — Quand la planoto se projotte sur le Soleil, je con- 
state qae Timagt^ c«^t noire, de toiute p^rfaitoment uniforme et k 
contours tK'a-nct« : elle conserve co niomo as}Hxrt |>cndant toate 
robscr\*ation. 



Dec. 1876. common to the TrantUs of 1769 and 1874. 53 

"A 21^ 18", temps moyen de Saigon, le cjontonr do 
Venus ext^rienr an disqne solaire s'illamine l^gerement, h 
oomxiienoer par le baa de Timage, qui reste constamment pins 
Tiaiblo qae le hant. La circonf^renoe plan^taire parait ainsi 
eompletee d*ane maniere tres-Ti&ible snr le ciel par cet are 
ImniDenx qui semble la continaer ezaoiement. 

^ Cet effet sabsiste qnand la planete avance ; peu & pea le 
disqne solaire, entre les bords voisins des deux astres, devient de 
phiB en plus obscnr a o6t^ du futur point de contact. Quand le 
moment dn contact approche, on ne distingue plus le bord du 
Soleil qui jusqu'alors se prolongeait nettement jusqu'au disqne 
^an^taire ; les deux comes de Techancmre sont s6par6es de 
reiMM par un intervalle obscur ; mais je continue k voir le bord 
de la planete, qui reste l^gerement luminense. Cette circon- 
£evence luminense me parait tangente an bord du Soleil, prolong^ 
par la pens^ dans I'ombre ; c'est le moment qui me semble ^tre 
oelni dn contact. La planete s'61oigne du bord du Soleil, laissant 
obscnr Finteryalle qui les s^pare ; un filet Inmineux yient com- 
pleter la ciroonf^rence du Soleil en reunissant les denx comes de 
Techancmre : Tombre qui persiste entre Venu$ et le Soleil n'est 

oompletement dissipee que vingt-trois secondes pins tard 

" Sortie, — Les images sont ondulantes ; n^nmoins comme le 
matin, les contours de la planete sont bien tranches ; sa teinte 
est oniform^ment noire. Quand Venus s'approcbe du Soleil, une 
ombre s'^tend entre les denx astres ; le bord du Soleil se rompt 
on deux comes an point ou doit s'efiectuer le sortie, et les con- 
kmn de deux astres en ce point deriennent invisibles. Je ne puis 
jnger dn moment du contact qu'en I'appr^iant de mon mieux, 
en continuant par la pens^ les parties invisibles des circonfS- 
rences ; de meme dans une observation an sextant d'une bauteur 
de Soleil, si le bout de Tastre est en partie masqu6 par un petit 
image, il arrive qu'on cberche a obtenir le contact an jnger. 

*' Quand la planete commence a ^merger j 'examine si sa 
circonference devient luminense, comme le matin : le pbenomene 
ne pandt pas se reprodnire. L'echancrure diminue de plus en 
pins ; pen a peu les ondulations du Soleil rendent son observation 

difficile, elle devient enfin invisible " 

Li these observations we have all the phenomena observed in 
1769 by Wales, Dymund, Hell, Chappe, Cook, and Green, repro- 
duced with modem instruments, and in the ejes of ob5^rver8 
who were certainly not biassed in favour of any views of mine. 
The fringe is here again the penumbra of Cook and Green. It 
may, perhaps, be remembered that Cook and Green, in 1 769, 
observed the geometrical contacts of a penumbra as dark, or 
nearly as dark, as that of the planet, and also the geometrical 
** contacts of the dark body of Venusy The following remarks 
of M. Herand are im{)ortant as bearing on these points, and on 
the gradual establishment of the contact : 

^ L'apparition dn filet Inmineux a ete pour ainsi dire gradn- 
elle ; de plus, comme je I'ai dit dans le proces- verbal, la sopa- 



54 ^^' SUmey On Phenomena of Inienial Contaeis xxxvn. 2^ 

ration de rimage noire et des franges ^tait plus netie, anssi nette 
an moins qne la separation des franges et I'image lomineuse dn 
Soleil, et j'ai en qnelqne peine k me d^fend^ de oonsid^rer 
comme le bord de VSnus la Umite de Timage noire, d'antant pins 
qne ces franges n'ont repam qne tr^lentement an point oii le 
contact s'6tait fait: et c'est ainsi qne j'avais not6 d'abord k 
I'entr^e le moment ou la partie noire de rechanomre me 
paraissait ronde et tangent an Soleil." 

It will be seen, therefore, that Mons. Herand had some 
difficnlty in refraining from making an observation of the contact 
with the so-called ^ dark body of Venus,** like that made by Cook 
and Grreen in 1 769, in addition to the geometrical contact of the 
outer boundary of VentM. M. Herand also remarks, ** Ponr M. 
Bonifay, Tare laminenz a persist^ jnsqn'an moment dn contact et 
pent-^tre jnsqn'a pres ce moment, tandis qne ponr moi il avait 
dispam : je dois dire qne, preoccnp^ de I'observation dn contact, 
]*avais nn pen perdn de yue la petite anr^ole, et je n*ai pas not-^ 
I'instant de sa disparition." M. Herand's remarks on this 
point agree with those made by Wales and Dymond; and I 
. should be prepared to accept them as representing fairly my own 
observations. 

*In discussions of Cook's and Green's observations before the 
appearance of my paper, the geometrical contacts of the pennmbra 
as dark, or nearly as dark, as the planet, were taken as *' real 
contacts" "the first or last appearances of any disturbance at 
the Sun's limb near the point of contact," or " the first or last 
appearance of the least visible thread of light." The contacts 
with the '' dark body of VernM " were taken as the apparent con- 
tacts. These interpretations appeared to me as unsatisfactory. 
If the pennmbra was as dark, or nearly as dark, as the planet, 
the observers who observed geometrical contacts without dis- 
covering any distinction between the penumbra, or fringe, and 
the central darker portions of the planet, must have observed 
also contacts with the penumbra. In this case Cook's geo- 
metrical contacts of the penumbra, instead of being real contacts, 
were apparent or geometrical contacts. 

A reference to the drawings, of which copies are given in my 
papers, will show that at the time of the geometrical contacts 
with the " dark body of Venus,** the disturbance of the Sun's 
limb extended over nearly a diameter of Ventis, and that the true 
geometrical contact could not be thus intended. But the point 
which, as much as any other, influenced me, in the interpretation 
put upon these observations, was the remark made by Cook, 
that " the contacts were made gradually, and the time noted 
was when the thread of light was wholly broke by the pennmbra." 
This showed that Cook and Green had seen the disturbances of 
the Sun's limb, before at egress, and, after at ingress, the pennm- 
bral contacts. It was clear, therefore, that Cook and Green's 

* This sentence is printed according to the MS., I»ut some correction is 
perhaps required. — [Ed.] 



Dec. 1876. common to the TrcunaiU of 1769 and 1874. 55 

contacts could not be real contacts In the same sense as those 
made by Wales and Dymond were. The confirmation of my 
TiewB, on the interpretation to be pnt on Cook's and Green's 
obseryations, afibrded by the observations of the French observers 
in 1874, is remarkable. 

Since the appearance of my paper I am not awai*e that any 
astronomer has seriously maintained the correctness of the inter- 
pretations which had previously been held with respect to the 
nature of the contacts observed by Cook and Green. One astro- 
nomer doubted the goodness of the observations, and was inclined 
to attribute the appearance of the penumbra to instrumental 
defects. The observations of the French observers appear to 
show that there is no longer any ground for such a suspicion, 
and that the observations of 1769 are as good, or very nearly 
indeed as good, as the corresponding observations of 1874. Any 
one who will take the trouble to study my papers in the Monthly 
'Notices for 1868, October, will see that the interpretation which 
I put upon the observations of Cook and Green is the most im. 
portant point in my work. In fisu^t, the only other step of any 
importance was the rectification of a similar mistake m Hell's 
observations, indicated by the fact that different interpretations 
Ittd been assigned to the word *' contactus," at the ingress and 
egress. 

Small and unimportant changes are easily enough made in 
aH mch work. But when any astronomer will prove that one or 
inore of the twenty internal contacts included in the ten com- 
plete durations observed in 1 769 has been erroneously interpreted 
DJ me, and will show that when my erroneous interpretation is 
amoved and the correct interpretation carried into the equations 
of condition, the ten durations are fairly represented, and that 
the value of the solar parallax deduced from the equations is no 
longer my value 8"'9i, or one differing ftx>m it by + o"*o7, but is 
Encke's value 8"*58, or one differing from it by ± o"'o7 — then 
I ahall be quite prepared to admit that my work has been without 
^ue. Before this is done I can only meet general statements 
that the work is not accepted, by asking those who assert that 
such is the case to ^o one stop further and prove that it ought 
not to be accepted. If the work is inaccurate, the proof should 
be easy ; but no proof of the kind has yet been given. 

Royal Obiervatory^ Cape of Good Hope, 
1876, November 6, 



56 Afr. Perry ^ On Diffraction ExperimmiU XXXYn. a, 

0/* some Diffraction Experiments of AT. Oh. Andre with reference to 
Astronomical Instruments^ and tlie General Theory of this 
Diffraction. Bj the Rev. S. J. Perry. 

My attention was first called to these experiments daring a 
visit I paid this year to France ; and whilst in Paris I had the 
pleasure of observing with the instmments, and of noting the 
extreme care with which the experiments are being made nnder 
the most favourable circumstances. Some of the experiments are 
confirmatory of results already noted by other astronomers, as 
by Sir W. and Sir J. Herschel and the Rev. W. Dawes, whilst 
others, as well as the complete theory of the subject, are, as far 
as I am aware, due entirely to the labours of M. Andre. 

The image of a luminous point in the focus of a telescope is 
known to be a central disk surrounded by bright rings, the 
diameter of the disk varying inversely as the aperture of the object- 
glass or mirror employed. Hence the limitation to the separating 
power of a given instrument. If, however, the centre of the 
field is covered, the diameter of the focal disk diminishes as the 
diaphragm is increased. The separating power is thus augmented, 
but the ratio of the intensity of the bright rings to that of the 
central disk is proportionately increased. 

If we draw a curve, whose ordinates represent the intensity 
of the light of each point of the image, and whose abscissas are the 
angular distances of these points from the axis of the telescope, 
this intensity curve, drawn for any particular aperture, will hold 
good for any other aperture, provided the unit for the abscissas 
is made inversely proportional to the aperture. A revolution of 
this intensity curve round its vertical axis will form what M. 
Andr6 calls the Solid of Diffraction ; and if the axis of this solid 
coincides with that of the telescope, the quantity of light on any 
element of the focal plane is proportional to the cylindrical 
portion of the volume of the solid of diffraction, the base of the 
right cylinder being the given element.* 

When the object is of finite dimensions, instead of being a 
luminons point, there is no interference of the rays from the 
different points, but the intensity of the light at any part of the 
image is the sum of the intensities of the separate elements. 
Hence we obtain the following theorem : — If the solid of dif- 
fraction, corresponding to the aperture employed, be placed so that 
its axis, which is perpendicular to the focal plane, passes through 
a point (771), the cylindrical portion of the solid, comprised within 
the geometrical image of the object, measures the intensity of 
(m). 

Applying this theorem to objects of different dimensions, 
we find that the intensity of the image of a brilliant straight line 
is measured by the surface of a section of the diffraction solid ; 

* The wi.lih of tlic soli 1 of iliffr.iction varies ineersely as tho aperture of 
the telescope. 



Dec. 1876. M, Andre, and on Theory of Diffraction. 57 

and that if the straight line is widened into a band, the measure 

of the intensity of the imaga is the volume of the same solid 

comprised between two sections, which widen out in the same 

proportion as the luminous band. Taking the more practical 

case of an object whose diameter is so considerable in every 

direction that we may consider the boundary lines as 

fltraight, we easily see that the focal image consists of two parts : 

One similar to its geometrical image, depending on its form 

and apparent dimensions, but increasing with the 

aperture ; the intensity being constant and TTHLYiTWTim 

throughout: 

The other overlapping and surrounding the first, its shape 

varying with that of the object, but its angular 

diinensions depending solely on the aperture. The 

intensity of this portion of the focal image, decreasing 

progressively, is reduced to one half at the limits of 

the geometrical image, and then quickly becomes 

insensible. 

To find the intensity at the difierent points of this zone 

of difiracted light, which surrounds the geometrical image 

of any object of sufficient apparent magnitude, we must cal- 

calate the successive portions of the volume of the solid of 

diffiraction intersected by a plane, which keeps parallel to the 

udg of the solid, whilst it moves from one edge of the zone to 

the other. As the extent of the zone of difPracted light bears a 

constant ratio to the maximum intensity of the focal image, the 

diameter of any body of sufficient brilliancy, observed on the same 

bickground, varies with the aperture. Thus for a 4-in. aperture 

the angular measure of the zone of diffracted light is i''*4, on the 

BQpposition that light, reduced to T^th of the central portion, 

ceases to affect the retina sensibly. Diameters are thus increased 

*''*8 by a 4-in. telescope. This correction, called the Constant of 

Instrumental Diffraction, differs from the separating power of the 

telescope, and varies with the aperture of the telescope and the 

hrilliancy of the object. 

In owier to verify experimentally these theoretical results, a 
hole was made in a piece of silvered copper, and a strong light 
from a Drummond lamp thrown upon it. Observing this by 
direct and reflected light, differences of 5'''82, 8''-87, and i3"-6o, 
^ere found with apertures of 6*5, 2*9, and 17 centimeters. 

A more accurate verification was made with a piece of 
hlaekened brass, in which two rectangular apertures had been 
carefiilly cut with bevelled edges, 3 centimeters in height by 1*5 
in breath, and 1*5 apart. Direct light was alone used, and 
^h apertures of 6*5, 3*0, and 17 centimeters, the exterior 
diameters were found to be I2i"'i5, I22"*i7, and I25"'86, and 
the interior ones only 36"'i3, 34''*48, and 3i"'46, respectively. 

Measures of the diameters of Mercury and Vemis, whilst the 
planets were crossing the solar disk, also lead to the same con^ 
elusions. 



58 Bev, S. J. Perry, On Diffraction Experiments efc. xxxTn. 2, 
Thus, in the Transit of — 







Obieryer. 


Inttruni6nt< 


Ax)6rture. 


mefwored. 


Unity of I 


Morcuiy 


4, 5 May 1832 


Bessel 


Heliometer 


o*i6o 


11-987 


6697 






Gambart 


Equatoreal 


0*070 


9-290 


5*184 


tt 


8 May 1845 


Mitchel 


tt 


0265 


11-580 


6-522 


•f 


ft 


Madler 


ft 


0*224 


II7S4 


6*542 


ft 


1* 


Schmidt 


tt 


0-068 


10-853 


6-057 


9f 


8, 9 Not. 1848 


Arago 


tt 


01 62 


10-155 




ft 


f» 


Dawes 


tt 


0'102 


9389 




ft 


ft 


tt 


ft 


0*072 


9369 




ft 


4 Not. 1868 


Wolf 


tt 


0-204 


9430 


6367 


ft 


ff 


Flnmmer 


ft 


0-165 


9-001 


6-077 


•t 


ff 


Stmve 


ff 


0*064 


6-840 


4*6i8 


VenuB 


8 Dec. 1874 


Mouchez 


ft 


0-217 


64*992 


16-993 


» 


ft 


Tennant 


ft 


0*152 


63948 


16-904 



Calonlating the constant of instrumental diffraction for a 4-iiL 
telescope &om the last observations of MerctMry and Venus, we 
obtain a mean yalne of 2" '634, which agrees closely with the 
theoretical valae of 2'' '80. If we compare the above diameters 
with measures taken at other times, we find that the diameter 
invariably decreases with the brilliancy of the baokgpx)nnd. 

The corrections applied to the lunar diameter, when rednoed 
from occnltations of stars by the Moon, observed at the Royal 
Observatory with the East Equatoreal, affords another confirmation 
of the correctness of the preceding conclusions. The correction 
adopted for stars observed at the dark limb is — 2'''54, and at the 
bright limb— o"-8o ; the difference is, therefore, i"74, whilst 
theory would give for the same instrument i"'55. 

When we increase the separating power of a lens bv means 
of a central diaphragm, the constant of instrumental dif&action 
is increased, on account of a change in the form of the solid of 
difh:uction, consisting in an increase of the relative volume of 
the parts external to the first minimum of intensity. If the 
aperture is thus reduced to ^, the decrease of light ceases to be 
continuous, and the constant of instrumental diffraction increases 
for a 4-in. telescope from 2"*8 to 4"-o. This has been verified by 
observations of the Moon and also of artificial objects. 

As the mathematical theory of the subject has been worked 
out fully in a published essay, it would be out of place to 
enter into the question here, especially as this short notice of the 
investigations of M. Andr6 is given mainly as an introduction to 
a second paper on a kindred subject. 



Dec. 1876. Bev. S, J. Perry, On Phsnouiena exhibited etc. 59 



On the Phenomena exhihittd hy a Planet in its Transit across the 
Solar Disk, from Observations made by M. Ch. Andr6. 

By tlie Rev. S. J. Perry. 

The resnlts contained in this paper have a special interest at the 
present time, as the experiments were made with the direct view 
of seeming accuracy of observation at the transit of Ventis in 
1882. We have bat a short time for making all the necessary 
preliminary preparations for this, onr only remaining chance of 
testing the vsJae of the transit of Venus methods for determining 
the solar parallax, and it is, therefore, well to learn what is being 
done elsewhere both as a guidance and as a spnr. 

The expedition of the Italians to India in 1874 was nnder- 
taken mainly with the object of testing the spectroscopic methods 
of observing the coming transit, and the volume printed by 
Signer Taccbini shows the success of their endeavours, and 
nrvee as an admirable guide for those who would prepare them- 
nlves for a fruitful campaign in 1882. Last summer I found that 
my own spectroscopes gave very satisfactory results with one of 
toe methods; and I purpose examining the others more in 
detail and under varying circumstances during the coming 
year. 

The experiments of M. Andr6 are being made under the most 
idvantageous circumstances. The splendid subterranean base- 
ment of the ficole Normale at Paris is placed at his disposal, and 
there, in a passage considerably more than too meters in length, 
be lias established his apparatus. This consists of a model of the 
^nuisit of an inferior planet ; the planet being moved by clockwork, 
ttd passing across the bright field backwards and forwards, 
without the necessity of any personal adjustment, and registering 
ttch contact electrically on a chronograph. The bright field 
which represents the Sun is illuminated by a Drummond light, 
lod as a supply of oxygen is always at hand, a special pipe 
having been kindly laid down by M. H. Ste. Claire de Ville from 
his chemical laboratory overhead, no delay or loss of time is ever 
experienced ; an advantage that will be fully appreciated by those 
who have made similar observations in the open air, with the 
Son itself as the source of light. Three telescopes are mounted 
at the distance of about 100 meters from the model, and the 
^ffonog^ph is established in an adjoining passage. The method 
^ observing is too obvious and too familiar to need any explana- 
fcn here. It will suffice to give at once the conclusions at which 
M. Andr6 has arrived, which I will take from a letter received from 
bim towards the end of last month. 

I. The bridge, black ligament, or black drop, as it is 
^vioDsly called, is a necessary phenomenon under certain cir- 
^omttances, and not merely accidental. With an unchanging 
■OQioe of Hght of sufficient brilliancy the angular dimensions of 

s 2 . 



6o Bev. 8. /. Perri/, On Phenomena exhibited etc. xxxvii. 2, 

the ligament are inversely proportional to the diameter of the 
object-glass, and with an aperture of 5-inches, the drop is scarcely 
perceptible. Diaphragms should never be used when observing 
Ventis in transit, as the apparent dimensions of the drop are 
augmented by any increase in the focal length. 

2. It is always possible to get rid of the ligament, and reduce 
the phenomena to geometrical contacts, either 

(a) by reducing sufficiently the intensity (^f the source of 

light, or augmenting the absorbing power of the dark- 
glass employed ; or again 

(b) by covering the object-glass with a network diaphragm, 

composed of rings alternately full and empty, and all 
very thin, but bearing a certain proportion to the focal 
length of the lens. 

3. The defect of imperfect focussing has bat little influence 
on the result, the phenomena changing little as long as a fair 
focus is obtained. 

4. Atmospheric undulations, on the other hand, have a con- 
siderable influence. They tend to give the image of the planet 
every description of strange form, and to them are due the con- 
tacts at several points at the same time, of which so much has 
been said. These are entirely got rid of by coating one of the 
anr&ces of the object-glass with a thin fllm of silver. 

5. Even when the object-glass is so small, and the dark-glass 
so thin, that the ligament is still present, the observation may 
still by good ti'aining be made very precisely. One phase of the 
phenomenon is simultaneous for all apertures, and can be esti- 
mated without difficulty to within 0*75 for interior contact at 
ingress, and i'*5 at egress, thus leaving a probable total error 
of 2**25 ^^ ^^® observed duration of the transit. 

6. In order to secure the solar parallax to within o"*oi, it 
suffices that the error in the duration of transit should not 
exceed 5* ; a small telescope may, therefore, serve to determine 
this parallax to within o'''oo5. Halley was not then mistaken in his 
estimate of the great value of his method. 

7. The above results agree perfectly with the theory of 
instrumental difl'raction, and can be rigorously deduced from it. 
To effect this, it is only necessary to draw the geometrical- 
phenomenon as it presents itself at the different epochs of 
the transit, and to measure the portion of the volume of the 
solid of diffraction comprised between Veniis and the Sun's 
edge. M. Andr6 has made the calculations for the epochs 10', 
5', o', and from the beginning and end of the transit. 

8. The phenomena are the same for Mercury as for Venus^ 
but the magnifying power must be greater for Mercury^ almost 
double. 

The difficulties that have so far surrounded the observation 
of the transit of Veyms have arisen mainly from the precon- 
ceived idea expressed in the sole word " Contact.'* The phe- 
nomenon could have been geometrical contact only in a restricted 



Dec. 1876. Mr. Marth, On the Orbit of a Centaur L 61 

number of cases ; and certainly our best resnlts are snch remarks 
18 those of F. Hell, when he describes the breaking of the bright 
line ; his words are clear, frank, and precise. 

Besides giving the telescope a sufficient apertnre, the 
maximani amonnt of light should also be obtained. It would be 
▼ell, therefore, if possible to determine accurately beforehand 
the exact thickness of dark-glasses most suitable for the observa- 
tion of the coming transit of VeniiSy and this might be obtained 
experimentally at the previous transit of Mercury, This last 
question of the dark-glass, which seems hitherto to have been con- 
sidered but of little moment, is in reality one of the most im- 
portant conditions in the obsei-vation. 

If I might add one remark to these useful conclusions of M. 
Indre, I should think it would be well to make experiments also 
as to the tint of coloured glass best suited for diminishing the 
light of the photosphere, without altering considerably that of 
tbe chromosphere, in order to give some value to the first 
external contact. Dr. Janssen has already shown us the feasibi- 
lity of this plan, and demonstrated that the spectroscope is not 
required in order to see Venua on the bright background of the 
diTomosphere. 



On the Orbit of a Centauri. By A. Marth, Esq. 
{From a Letter to E, Dunkin, Esq,, F.R.8.) 

At the close of the last meeting of the Royal Astronomical 
Society you proposed that I sliould furnish in writing the sub- 
stance of some remarks on the Double Star a Centauri ^ which I 
bd been permitted to address to the meeting just before. 

Though it has been pointed out some years ago that the comes 

of a Centauri would reach its apparent periastre in the course of 

the year 1875 ; ^^^ though the great importance of securing series 

of good observations during the preceding and following years is 

i^ecognised and appreciated by all who keep themselves informed 

on the subject of binary stars ; there seems cause to apprehend 

that the observers in the Southern Hemisphere, who alone are 

&Tourably situated for making such observations, have persisted 

in their strange neglect of this the most interesting of all double 

stars. Thinking that it might do some good, and could do no 

harm, if the subject were brought before the meeting, and if 

the personal friends of the Southern obscr\xrs were appealed 

to for their friendly assistance, I asked leave to occupy a few 

minutes before the adjournment with a short statement of the 

circumstances of the case, and to exhibit a diagram which would 

render any detailed explanation superfluous. In order to enable 

readers of this letter to reconstruct the diagram (and they will 

find it far more instructive and satisfactorv if thev themselves 



6tf 



Mr. Marth, On the Orbit of a Centaurl, xxxyn. 2, 



draw it on a larger scale on squared paper than if thev got it 
ready printed on a small scale), I subjoin the rectangular co- 
ordinates of a sufficient number of points of both the true and 
the apparent orbits, so that the two ellipses may be easily drawn 
by hand. The co-ordinates have been deduced from Mr. Powell's 
elements published in the Monthly Notices, vol. xxz. page 192, 
the line of nodes common to both ellipses being taken as ike 
basis. The x co-ordinates are consequently the same for both 
ellipses, while the (y) co-ordinates of the projected or apparent 
ellipse have a constant ratio to the y co-ordinates of the true 
ellipse. The first column of the table contains the corresponding 
true anomalies v of the comes : — 



V 



X 


(y) 






300*80 


+ 8-96 








Node. 


330 


+ 669 


+ 374 


+ o*57 







+ 372 


+ 6*23 


+ o*95 


Perihelion. 


30-80 





+ 768 


+ 1*17 




49-91 


- 276 


+ 7*96 


+ 1*22 


Maximum of y. 


70 


- 6*17 


+ 7*57 


+ 1*15 




90 


— 10*22 


+ 609 


+ 0-93 




no 


-14-96 


+ 285 


+ 0*44 




I20'80 


— 17-96 








Node. 


12975 


-19-88 


- 313 


-0-48 


End of minor axis. 


140 


— 22-03 


- 7-67 


-I-I7 




154-12 


-23-41 


-1539 


-2-35 


Maximum of 4r; 


170 


— 2I-00 


-2433 


-371 




180 


— 16-90 


-28-35 


-4"33 


Aphelion. 


191*69 


— 10-4* 


- 30*08 


-4*59 


Maximum of y. 


200 


- 5-59 


— 2929 


-4-47 




210-80 





— 26-40 


-403 




220 


+ 373 


- 23 02 


-3-51 




230-25 


+ 6-70 


- 18-98 


— 2-90 


End of minor axis. 


240 


+ 8-54 


-15-27 


-233 




250 


+ 963 


-1180 


-r8o 




26748 


+ 10-23 


- 673 


-103 


Miiximum of x. 


270 


+ IO*22 


— 609 


-o*93 




290 


+ 9*59 


^^^ • 


-0-28 




Centre of 1 
ellipse J 


- 6-59 


- 1106 


— 1-69 




The circle of declination passes 


through the 


points — 


North r = 


+ 20 y = 


- 903 






South 


— 20 


+ 903 







Dec. 1876. Mr. Marth, On the Orbit of a Oentcmri. 



6s 



The co-ordiuates of the chief positions of the comes, which 
have been deduced from observations, and have been published, 
aze the following (vide Monthh/ Notices, vols. xv. p. 88, zvi. p. 120, 
xvii. p. 19, xxiv. p. 170, and Memoirs, vols. xziv. zxv. and zxxii.) 



Time. 


X 

It 


1826*012 


-22'l8 


30t>12 


— 19*60 


3479 


- 16-87 


37*34 


- 15*46 


46866 


- 850 


48*023 


— 6*70 


50*926 


- 4*12 


53"049 


— 205 


54-003 


- 130 


55-318 


+ 0*09 


56015 


+ o*54 


56591 


+ i*ii 


59-382 


+ 3-67 


60*114 


+ 4-41 


60*479 


+ 4*55 


61052 


+ 5*08 


61*305 


+ 5*31 


61*576 


+ 5*45 


62*205 


+ 6-09 


63*028 


+ 6-63 


64*110 


•*• 7*44 


1870*1 


+ IO-22 


Predicted Positions. 


1872-0 


It 
+ 864 


730 


+ 6-88 


740 


+ 431 


75*0 


+ ri6 


76-0 


- 2-17 


77-0 


- 528 


18780 


- 807 



J! 


ObsoTor* 


PlAoe. 


-3*47 


Dunlop 


Pkuramatta 


-3*71 


Johnson 


St. Helens 


-4-27 


Herschel 


Feldhaosen 


-455 


ft 


tt 


-4-91 


Jacob 


Madras 


-4-46 


ft 


tt 


-433 


ft 


tt 


—4-06 


»i 


tt 


—401 


Jacob & Powell ,, 


-4-07 


Powell 


»» 


-3*77 


Jacob 


tt 


-3.72 


tt 


St 


-3*57 


Powell 


tt 


-3*58 


f» 


1* 


-3*26 


It 


tt 


-3-33 


t* 


tt 


-320 


tt 


tt 


-315 


ft 


tt 


-301 


H 


It 


-280 


t< 


tt 


— 2-50 


»» 


tt 


—0-69 


tt 


tt 



r. 

+ 0'II 

+0*52 
+ 089 

•HI3 

+ I-2I 

+ ri8 
+ 107 



The first four of these places have been observed in the 
Southern Hemisphere, all the others at Madras, where a Gentauri 
does not reach an altitude of 17° above the horizon. Powell's 



I 



64 Messrs, Wilscyn, and GledhiU, List of Binaify Sturs, xxlvil. 2, 

published observations represent upwards of 2,000 single 
measures (vide Mefmoirs^ vol. xxxii. p. 93). Of his later observa- 
tions made afber 1864, ^^J ^^ normal place for 1 870-1 seems 
to have become publicly known. It is to be hoped that he may 
have been able to watch and observe the comes of his favourite 
doable star tlirough the most interesting portion of its orbit ; bat 
with the star so near the horizon and with a 4-inch telescope, the 
task cannot but have been beset with considerable difficulties. Mr. 
Powell will have desenred all the more credit and honour. It 
might fairly have been expected that observers who are provided 
with better instruments, and are far more favourably placed 
for observing a Ceniauri, would have rejoiced at having the 
opportunity of observing it just during those years when 
the observations are of the highest permanent value. If Mr. 
Powell's orbit and remarks were not suiTicient to attract their 
attention, a glance over the Ephemeris deduced by Mr. Hind 
from Powcirs elements, and published in the Monthly Notices 
for November 1872, vol. xxx. page 54, might have shown them 
the lucky and important chance within their grasp. The observa- 
tions need not have interfered with other work, as they demand no 
fixed days and hours, and might liave been made in daytime. But 
it seems that the most favourable time and opportunity has been 
allowed to slip away unused. However, as a couple of position- 
angles which Lord Lindsay has obtained in 1874 during his 
Mauritius expedition, are said to indicate that the comes of 
a Ceniauri is more than half a year behind its predicted position, 
the Southern observers may have a chance of regaining a portion 
of their neglected opportunities ; and I suggested, therefore, 
that their personal friends should call their attention to the 
matter. But as you and other members of the Council have 
expressed the opinion that it would be better that I should put 
my remarks on paper for the Monthly Notices, I defer to your and 
their opinion, and I place accordingly these lines at your dis- 
posal, in the hope that they may be of some service. 

1876, December 13. 



A Preliminary List of Binary and oilier interesting Double Stars. 

By J. M. Wilson, Esq., M.A., aud J. Gledhill, Esq., F.R.A.S. 

The following list is intt^ndod to be the basis of a working 
List of Binary and other interesting Double Stars, of which it is 
desirable to have accurate measures at not very distant intervals 
of time ; and we think it may be of assistance to those observers 
who take up this branch of astronomy to have such a list for 
their guidance. We publish it also, with the hope that it may 
attract the attention of those who have specially devoted them, 
selves to the measurement of binary stars, and that they will by 
their criticisms point out any errors that may exist in it^ of 



Dec. 1876. Messrs. WUsati and OledhUL List of Binary Stars. 6^ 

omission or otherwise. It is our intention to offer to the Society, 
at no distant period a list of binaries and other interesting 
doable stars, with all the measures of them, that have been pub- 
lished up to the present date, extracted from the various Memoirs, 
Transactions, Journals, etc., which an astronomer must now con- 
salt if he wishes to ascertain the past history of a binary star 
and compute its orbit. It is plainly desirable that this list should 
be as complete as possible, and we shall be greatly obliged to 
Kay one who will pomt out to either of us any omissions in this 
preliminary list. 

With a view to this work, we formed, some years ago, a list 
0! double stars for observation, selected from those observed by 
2, 02, Madler, Dawes, Dembowski, Secchi, and others, and 
have measured them, in order to ascertain, in all doubtfal cases, 
whether there was sufficient evidence of appreciable change 
having taken place since the earliest measures. In this way we 
have been enabled to strike off many that were classed as pro- 
bable binaries by Madler and Secchi, and have ascertained that 
others are in motion which were not previously given in lists of 
Boch objects. Clearly, however, no list published now, however 
perfect, can possibly be final ; it can do no more than repre- 
sent knowledge up to the present date. 

In addition to the well-known Lists of Double- Star Measures, 
we have been enabled, at the request of the Rev. R. Main, 
to obtain from Herr Otto von Struve the yet unpublished 
Part I. of his forthcoming great work on Double Stars. The 
Part received contains the Pulkova measures of 2*s Doable 
Stars. Part II., containing the. re-examination of OS's own 
^wcoveries, is expected shortly. We have found this work of 
▼ery great help in deciding several doubtful points. 

The numerous close pairs discovered by Mr. S. W. Bumham, 
of which measures have been published, will be entered on this 
^. There can be but little doubt that these interesting and 
dimcnlt stars will shortly yield a rich harvest of binaries. 

A few words on the form of the list may here be given. The 
first column contains the reference number ; the second, the name 
of the star ; the third, ii*s or 02*8 number (the latter in brackets) 
where the star has been observed by either; the fourth, the 
fiumber in Sir John Herschol's great Catalogue, lately edited by 
the Rev. R. Main and Prof. Pritchard. 

In conclusion, the points on which we request information 
•le— 

(t) Binaries omitted which it is thought should appear in 

such a list. 
{2) Criticisms on the insertion of any stars which it is thought 

should be omitted. 
(3) Unpublished measures or orbits of any binary stars. 
Communications may be sent to J. M. Wilson, Temple 
Obiervatory, Rugby ; or to Mr. J. Gledhill, Mr. E. Crossley*8 
ObKrvatory, Uahfax. 



66 Messrs. Wilson and OledUU, List of binary Stars, xlxvn. 2, 



No. 


Name of Star. 


r 8 No. 


H*bNo. 


I 


Oephei 316(B) 


2 


2 


2 


••• ••• 


[2] 


35 


3 


Cephei 318 (B) 


13 


48 


4 


••• ••• 


16 


58 


5 


••• ••• 


[4] 


59 


6 


••a ••• 


23 


66 


7 


26 Andromedae 


[5] 


76 


8 


42 Piscium 


27 


103 


9 


Gassiopeise 49 (B) 


30 


127 


lO 


49 Piscium 


32 


156 


II 


X Gasfliopeiae ... 


[12] 


162 


12 


« • • •• • 


[18] 


242 


13 


i| CSassiopeise ... 


60 


283 


14 


.«. ••• 


69 


307 


15 


36 Andromedse... 


73 


319 


i6 


P. 0. 251 


80 


344 


17 


• • • « • • 


86 


373 


i8 


Ceti 160 (B) ... 


91 


393 


19 


PolariH 


93 


400 


20 


••• •• • 


[24] 


407 


21 


... ... 


[28] 


430 


22 


.• • • • • 


102 


453 


23 


42 Ceti 


"3 


' 474 


24 


••• .•• 


118 


502 


25 


• • • • • ■ 


122 


514 


26 


... ... 


125 


515 


27 


*• . ... 


132 


542 


28 


Andromedee 219 (B) 


133 


543 


29 


P. I. 123 


138 


568 


30 


• • • •• • 


142 


588 


31 


• « • • • • 


[35] 


606 


32 


• • • •• • 


158 


637 


33 


• • • •• • 


175 


677 


34 


• • • • • • 


183 


704 


35 


• • • • • • 


185 


710 


36 


P. I. 209 


186 


714 


37 


• • • • • • 


196 


738 


3S 


Piscium 


202 


753 


39 


y AndiMmedfiB ... 


[38] 


755 



Dec. 1876, Messrs. WHsan and GledhtU, List of Binary Stars. 67 



No. 


Name of Star. 


r 8 No. 


H'8 Ko. 


40 


10 Arietifl 


• • • 


208 


761 


41 


• • • 


• • • 


221 


799 


42 


Andromeds 259 (B) 


228 


818 


43 


66 Cell 


• •• 


231 


821 


44 


• •• 


• • • 


234 


827 


45 


• • ■ 


• • • 


257 


892 


46 


1 Casfliopeise 


• • • 


262 


906 


47 


• • • 


• • • 


278 


949 


48 


84Ceti 


• • • 


29s 


1009 


49 


• Fenei 


• • • 


296 


lOIO 


50 


yCeti 


• • ■ 


299 


1019 


51 


Arietis 1 14 (B) 


305 


1036 


52 


••• 




312 


IQ44 


53 


ir Arietis 




311 


1047 


54 


Fenei 85 (B) 




314 


1053 


55 


•• • 




[48] 


1058 


56 


• • • 




326 


1080 


57 


••• 




328 


1084 


58 


ff Arietis 




333 


1098 


59 


• • • 




334 


1 104 


60 


Persei 104 (B] 


|... 


336 


1 109 


61 


Procyon 








62 


• • • 




[50] 


1132 


63 


• • • 




355 


1 147 


64 


«• • 




367 


1179 


65 


• • • 




377 


1210 


66 


• • • 




380 


1222 


67 


• • • 




388 


1240 


68 


• • • 




400 


1270 


69 


• • • 




403 


1271 


70 


• • • 




408 


1279 


71 


7Tauri 




412 


1288 


72 


F. III. 98 




422 


1308 


73 


• • • 




447 


1370 


74 


F. III. 165 




[64] 


1387 


75 


Cephei 49 (H< 


?v.) 


460 


1406 


76 


32 Eriduni 




470 


1436 


77 


P. III. 242 




1531] 


i486 


78 


■ • • 




511 


1528 



6i Me98r8. WHson and OledhiU, List of Binary Stars, xxxvii. 2, 



No. 


Nome of Star. 


mHo. 


H'sNo. 


79 


• • « 


• •« 


[78] 


1540 


80 


40 EriduDi 


• • ■ 


518 


'553 


81 


■ • • 


• • • 


179] 


1571 


82 


■ • • 


• • • 


[80] 


1582 


83 


Tauri 230 (B) 


■ • • 


53S 


1600 


84 


• • • 


• •• 


[82] 


t6o2 


85 


• •• 


• • • 


[85 1 


1677 


86 


2 Camdopartl} 


ili 


566 


1687 


87 


• • • 


• • ■ 


567 


1690 


88 


• •• 


• • • 


577 


»7»5 


89 


• • ■ 


• p • 


61S 


1S31 


90 


• • • 


• « • 


619 


1842 


91 


5 AUTig3l> 




[9^] 


1844 


92 


•• • 


«■ • 


[93] 


1862 


93 


• •• 


• •• 


629 


1871 


94 


Camelupurdali 


19 (^Hev 


•) 634 


1S92 


95 


P. IV. 288 


• • • 


[95] 


1897 


96 


••• 


• • • 


[97] 


1903 


97 


14 Ononis (t) 


• •• 


[981 


1923 


98 


•• • 


• • • 


644 


1925 


99 


•• • 


• • • 


[100] 


1941 


100 


... 


• • • 


651 


1947 


lOl 


A Aurigse 


• •• 


• • • 


199 1 


102 


•« • 


• • • 


676 


2001 


103 


.• . 


• • • 


677 


2005 


104 


Tj Orionis 


• • • 


• t • 


2071 


105 


.* • 


• • • 


712 


2091 


106 


32 Orioir»< 


• • • 


728 


21SS 


107 


Tauri 380 (B) 


• • • 


742 


2165 


108 


•' Orion IS 


• • • 


748 


2178 


109 


• • . 


• • • 


749 


2182 


no 


*• • 


• • • 


[112] 


2lijO 


III 


C Ononis 


• ■ • 


774 


2235 


112 


... 


• • • 


3^5 


2237 


"3 


■ ■ • 


• • • 


853 


24C2 


114 


... 


• • • 


861 


2475 


"5 


4 Lyncis 


• • • 


881 


^527 


116 


• • • 


• • • 


932 


2695 


117 


• • • 


• •• 


945 


2730 



Deo. 1876. Messri. Wilson and GfledhUl, List of Binary Btan, 69 

No. NameofSUr. rsNo. H*«No. 

118 54Aurig«B ... [152] *734 

119 12 Lyncis ... 948 2749 

120 ... ... 3"7 2757 



137 



H7 



[154] 2766 

[I 551 2785 



121 
122 

123 ... ... [156] 2795 

124 Sirius ... ... 2799 

125 i4L3mci8 ... 9^3 2802 

126 ... ... [157] 2811 

127 13 Lyncis ... [i59] 2851 

128 ... ... [161] 2869 

129 

130 

131 31 1037 ... [166] 3012 

132 ... ... 1049 3040 

133 P. vu. 52 ... [170] 3068 

134 ' Geminorum ... 1066 3084 

135 ... ... 1071 3092 

136 ... ... ^074 3103 



38 Geminorum (e) 982 2872 

fi Canis Majoris 997 2899 



1076 3107 



138 ... ... >o8i 3121 

139 ... ... 1091 3158 

140 ... ... 1093 3161 

141 
142 

143 
144 

145 



I 104 3214 

Castor ... mo 3228 

P. VII. 170 ... 1 126 3297 

jc Geminorum ... ['79] 3321 

1136 3340 



146 ... ... "42 3354 



I 157 3420 



,48 ... ... [186] 3482 

149 Lyncis 8s (B) ... 1187 3533 

150 fCaneri ... "96 3557 

,51 P. vm. 13 ... >202 3572 

1216 3646 

[193I 3696 



152 

153 

154 

155 

156 ... ... 1287 3907 



1263 3832 
fHydne ... I273 38^8 



70 MesBTB. WiUon and Oledhill, List of Binary Stars, xxxvn. 2, 



Jffo. 


Name of Star. 


TsNo. 


H*8No. 


157 


1 Un» Majoris 


[196] 


3943 


158 


•• • ••• 


1300 


3970 


159 


a* UnsB Mi^'oris 


1306 


3989 


160 


•• • « * • 


1316 


4021 


161 


«•• ••• 


1321 


4046 


162 


••• ••• 


3121 


4083 


163 


LyDcis 157 (B)... 


1338 


4101 


164 


••• •• ■ 


[200] 


4123 


165 


■« • •• • 


[201] 


4128 


166 


HjdnB 116(B)... 


1348 


4139 


167 


wLeonis 


1356 


4165 


168 


flydwB 134 (B)... 


1365 


4190 


169 


P. IX. 161 


1377 


4253 


170 


p UmeMigoris 


[208] 


4290 


171 


.«• •• • 


1385 


4294 


172 


••• ••• 


1389 


4305 


173 


8 Seztantis 


A.C. 5 


4314 


174 


••• ••• 


1406 


4387 


175 


a* a •• a 


["31 


4429 


176 


P. X. 23 


[ai5] 


4449 


177 


y Leonifl 


1424 


4469 


178 


Leonis 145 (B)... 


1426 


4477 


179 


• • • « • • 


1439 


4536 


180 


• •• • • • 


1457 


4606 


181 


P. X. 128 


[224] 


4612 


182 


•■• • •• 


1472 


4669 


183 


• ■ • • • • 


[228] 


4671 


184 


• • • ■ • • 


[229] 


4690 


185 


• • • ■• • 


i486 


4714 


186 


■ •• ■• • 


[230] 


4717 


187 


54 Leonis 


1487 


4719 


188 


• aa aa a 


1500 


4754 


189 


PaXa229 


1504 


4782 


190 


• • • • • • 


1514 


4820 


191 


[539] 


1516 


4833 


192 


P. XIa 9 


1517 


4834 


193 


( Vzmt Migoris 


1523 


4860 


194 


aaa aa a 


1534 


4885 


ifS 


I Lsoais 


1536 


4896 



Dec 1876. Messrs. Wilson and OledhUl^ List of Bvnary Stars. 71 



No. 


Name of Star. 


TbNo. 


H'sNo. 


196 


57 Ursee Midoris 


1543 


4924 


197 


• • • • • • 


[234] 


4934 


198 


• • • • ■ • 


[235] 


4942 


199 


P. XI. Ill 


1555 


4978 


200 


• • • • t • 


[237] 


5000 


201 


• • • • • ■ 


1588 


5141 


202 


••• •• ■ 


3123 


5167 


203 


•»• «•■ 


1607 


5205 


204 


Comae Ber. 68 (B) 


1639 


5293 


205 


• • • • • • 


1641 


5296 


206 


••• ••• 


1644 


5307 


207 


Virginis 191 (B) 


1647 


5319 


208 


• • ■ •• • 


1658 


5341 


209 


••• ••• 


1663 


5354 


210 


y Viiginis 


1670 


5377 


211 


■• • t • • 


1678 


5401 


212 


35 Conue Ber. ... 


1687 


5430 


213 


••• ••• 


[256] 


5445 


214 


179 Comie Ber. 


1722 


5515 


215 


42 Comee Ber. ... 


1728 


5523 


216 


« • . ... 


[261] 


5535 


217 


... ... 


1734 


5570 


218 


... • • * 


1742 


5590 


219 


.•• ... 


1746 


5608 


220 


72 Virginis l^ ... 


1750 


5622 


221 


P. xni. 127 ... 


1757 


5639 


222 


25 Canum Yen. 


1768 


5673 


223 


84 Virginis 


1777 


5704 


224 


• • • • • ■ 


1 781 


5726 


225 


r Bootis 


[270] 


5737 


226 


... ••• 


1785 


5754 


227 


p.xm. 238 ... 


1788 


5789 


228 


[277] 


1812 


5894 


229 


... ... 


1819 


5907 


230 


... ... 


1820 


5913 


231 


Bootis 121 (B)... 


1825 


5922 


232 


•a. ••. 


1830 


5933 


233 


... •• • 


1832 


5934 


254 


P. XTV. 70 ... 


1837 


5964 



72 Messrs. WiUon and GledhiU, List of Binary Stars, xxxvii. J. 



No. 


Name of star. 


l'« No. 


H*8No. 


235 


• • . •• 


1842 


5987. 


236 


• • • . . 


1858 


6040 


237 


• • • *• 


1863 


6062 


238 


X Bootis 


1864 


6066 


239 


fBootis 


1865 


6069 


240 


• • • • • 


1866 


6072 


241 


• • • ■ • 


1876 


6099 


242 


c Bootis 


1877 


6101 


243 


• • • • • 


1879 


6106 


244 


• • • « • 


1883 


6124 


245 


1 Bootis 


1888 


6146 


246 


• • • • ■ 


[287] 


6159 


247 


• • • •• 


[288] 


6161 


248 


44 Bootis (i) .. 


1909 


6237 


249 


• • • • • 


1925 


6305 


250 


• • • • • 


[295] 


631 1 


251 


5 Serpen tis 


1930 


6327 


252 


Coronee i (B) .. 


1932 


6331 


253 


••• . • 


1934 


6336 


254 


ri Coronse 


1937 


6362 


255 


P. XV. 74 


1938 


6371 


256 


• • • • • 1 


1944 


6382 


257 


■ t • • • 1 


[296] 


6388 


258 


5 Serpentis 


1954 


6426 


259 


■ • • • • < 


1957 


6434 


260 


••• • • 


[298] 


6446 


261 


•• • .* 


1961 


6440 


262 


7 Corone 


1967 


6469 


263 


• • • t ■ 1 


1983 


6523 


264 


• « • • • 


1985 


6535 


265 


18 ir« Ursa Mine 


ris 1989 


6547 


266 


... • • « 


[303I 


6575 


267 


1 Librae 


1998 


6582 


268 


K Hercalis 


2010 


6610 


269 


49 Serpentis 


2021 


6634 


270 


•• • • • • 


2022 


6640 


271 


••• • • 


2026 


6645 


272 


a Coronse 


2032 


6654 


273 


Antares 


• • t 


6707 



Dec. 1876. Mestnrs, Wilson and OledMU^ List of Binary Stars. 73 



No. 


Name of Star. 


TbNo. 


H'aNo. 


274 


•a ■ •.• 


2049 


6718 


275 


Draconifl 99 (B) 


2054 


6723 


276 


X Ophinchi 


205s 


6727 


277 


CHercnlis 


2084 


6799 


278 


• • • • • • 


2094 


6816 


279 


• B • • • • 


2097 


6823 


280 


21 Ophiuchi ... 


[315] 


6840 


281 


• • • • • • 


2106 


6842 


282 


Herculis 167 (B) 


2107 


6847 


283 


• ■ • • • • 


3107 


6867 


284 


■ • • ■ • • 


[321] 


6879 


28s 


P. XVI. 270 ... 


2114 


6888 


286 


20 Draconifl ... 


2118 


689s 


287 


Herculis 210 (B) 


2120 


6910 


288 


ft Draconis 


2130 


6935 


289 


36 Ophiuchi ... 


... 


6946 


290 


8 fleiculifl 


3127 


6968 


291 


... ... 


2145 


6973 


292 


p Herculis 


2161 


7016 


293 


• •• •• • 


2165 


7028 


294 


• • • • ■ • 


2173 


7040 


29s 


P. XVII. 163 ... 


2190 


7076 


296 


... ... 


2199 


7104 


297 


... ... 


2203 


7108 


298 


... ... 


2205 


7128 


299 


• . . ... 


2214 


7129 


300 


... ... 


2215 


7130 


301 


ft Herculis (A. C. 7) 


2220 


7142 


302 


r Ophiuchi 


2262 


7245 


303 


■ • • • • • 


2267 


7262 


304 


•• • ••• 


2271 


7267 


30s 


70 p Ophiuchi ... 


2272 


7273 


306 


73 Ophiuchi ... 


2281 


7309 


307 


HercuHs 417 (B) 


2289 


7322 


308 


• • • • • * 


2294 


7340 


309 


Lalande 33731... 


2303 


7370 


310 


... ... 


231 1 


7388 


311 


Herculis 452 (B) 


2315 


7406 


312 


39 Draconis, b .. 


2323 


7425 



74 Messrs. Wilsofi and OledhiUy List of Binary Btars. xxxm. 2, 



No. 


Name of Star. 


2*8 No. 


H'flNo. 


313 


^ Draconis 


[353] 


7443 


314 


••• «•< 


[358] 


7479 


315 


aLyrsB 


• • • 


7501 


316 


• • • • • 1 


2367 


7523 


317 


• • • •• < 


2384 


7563 


318 


f* Lyne 


2382 


7564 


319 


t'LyrsB 


2383 


7S66 


320 


• •• • • 


2396 


7593 


321 


•• • • • 1 


2400 


7604 


322 


• • • • ■ 


2402 


7609 


323 


• • • • • 


2409 


7625 


324 


Snconu 


2420 


7660 


3^5 


[36S] 


3130 


7670 


326 


•• • ••« 


2422 


7671 


327 


II Aqnils 


2424 


7675 


3*8 


• ■ • • ■ « 


2429 


7689 


329 


P. xvm. 274... 


2434 


7702 


330 


• • • • • ■ 


2437 


7706 


331 


p. XVIII. 287... 


2438 


7709 


332 


• % • • • fl 


2441 


7723 


333 


• • • ••« 


2454 


7752 


334 


Lalaode 35821... 


2455 


7753 


335 


• ■ • •• I 


2464 


7768 


336 


• • • • • < 


2471 . 


7787 


337 


%• • • • 


2481 


7810 


338 


• • • •• 4 


2484 


7819 


339 


Cygni 6 


2486 


7828 


340 


« • • p ■ ■ 


2491 


7854 


341 


• • • • • 


2514 


7922 


342 


P. XIX. 128 .. 


2521 


7946 


343 


Cygni 22(B) ... 


2525 


7958 


344 


•• • • • I 


2538 


8006 


345 


P. XIX. 185 .. 


2S4I 


8024 


346 


• •• •• 


2544 


8037 


347 


• • • • • 1 


[378] 


8061 


348 


• • • • • 1 


2556 


8079 


349 


• • • • • 1 


[383] 


8123 


350 


p • • • • 


2574 


8139 



Dec. 1876. Messrs. WHsan and OledMll, List of Binary Btaars. 75 



No. 


Hameof Star. 


3'iNo. 


H'a No. 


351 


• • • • • • 


2576 


8146 


352 


8 Cygni 


2579 


8153 


353 


• • • • • • 


[387] 


8179 


354 


iS AqTiils 


[532] 


8228 


355 


Cygni 1 16 (B) [392] 


2607 


8274 


356 


• • • • • • 


2619 


8313 


357 


tfSagittsB 


2637 


8382 


358 


••• • • • 


2640 


8386 


359 


.• . ... 


[400] 


8411 


360 


■•• ... 


2658 


8457 


361 


P. XX. 178 [407] 


2690 


8600 


362 


• • • • • • 


2696 


8624 


363 


/S Delphini 


2704 


8663 


364 


K Delphini 


[533] 


8674 


365 


... ... 


2708 


8692 


366 


•.• ... 


[410] 


8703 


367 


•■• ••• 


2725 


8751 


368 


52 Cygni 


2726 


8755 


369 


A Cygni 


[413] 


8773 


370 


4 Aquarii 


2729 


8784 


371 


... • • • 


2734 


8812 


372 


« Eqnulei 


2737 


8839 


373 


... • • • 


2744 


8860 


374 


... • • • 


2746 


8868 


375 


... • • • 


2749 


8876 


376 


61 Cygni 


2758 


8898 


377 


• • • • • • 


2760 


8902 


378 


8 Equnlei [535] 


27V7 


8959 


379 


... • • • 


2779 


8965 


380 


P. XXI. 50 ... 


[432] 


8976 


381 


A. C. 19 


• • • 


8998 


382 


• • • • • • 


2793 


9048 


383 


• • • ••• 


[437] 


9021 


384 


Pega8i20(6) ... 


2799 


9072 


385 


• • • • • • 


2801 


9087 


386 


Pegasi 29(B) ... 


2804 


9107 


387 


• • • • « • 


[443] 


9134 


388 


• • • • • • 


[447] 


9175 



F 2 



76 



Messrs. 


Wilson and Gledhill, List 


of Binary 


Stofv. xxr 


Ko. 


N«me of Star. 


7b No. 


H'aNo. 


389 


Mpygni 


• • • 


2822 


9210 


390 


• . . 


• • • 


2825 


9226 


391 


• • • 


• •• 


2828 


9240 


392 


... 


• • • 


2837 


9273 


393 


... 


• • • 


2849 


9333 


394 


... 


• • • 


2865 


9416 


395 


P.XX. II, 12 


• • • 


2872 


9442 


396 


p. xxn. 33 


• • • 


2877 


9469 


397 


Pegasi 148 


• •• 


2878 


9466 


398 


••. 


• • • 


2895 


95 16 


399 


33Pega8i 


• ■ • 


2900 


9539 


400 


CAqoarii 


■ •• 


2909 


9580 


401 


37Pegasi 


• • • 


2912 


9593 


402 


• •• 


• • • 


291S 


9614 


403 


• • • 


• • • 


2928 


9670 


404 


■ • • 


• • • 


2934 


9703 


405 


• • • 


■ • ■ 


2942 


9736 


406 


P.XXTT. 219 


• • • 


2944 


9742 


407 


• • • 


• •• 


[536] 


9832 


408 


52 Pegasi 


• • ■ 


[483] 


9840 


409 


• • • 


• • • 


2976 


9901 


410 


• • • 


• • • 


2990 


9946 


411 


94 Aqoarii 


• • • 


2998 


9982 


412 


Gephei 


• • • 


3001 


9993 


413 


• • • 


• ■ • 


3006 


10004 


414 


• • • 


• • • 


3007 


10015 


41S 


P. xxin. 69 


• • • 


3008 


10020 


416 


••• 


• •• 


[500] 


10117 


417 


• •. 


• • • 


3037 


10170 


418 


•• . 


• • • 


3046 


1023s 


419 


37 Andromeda 


:(B) 


3050 


10258 


420 


Lalande 47206 


... 


3056 


10291 


421 


• • • 


• • • 


3062 


10304 


422 


• •• 


• • • 


[523] 





[. 2 



The following stars, haying common proper motion (see 

Stmye's Pos, Med,) may, perhaps, be measured occasionally with 

advantage, and should therefore be inserted in the list. The 

^t<moe6 are between 32" and 7' : 40 Eridani, xjj Aqttarii, 37 Oeii, 



Dee. 1876. Mr, Darwin, On Oversight in Mecanique Oeleste etc, 77 

Begitlus, 16 Cygm, Castor, r^, v^ Draconis, 1 Pegasi, i Bootis, 
93 Leonisy /x Bootis, 0^, 6^ Tauri, e and 5 LyroB, a Tawri, 6 and 8 
Yulpec,, 16 and 17 Dracanis, 33 and 34 Ophitushi, a' and 
a' Capricomi ; also P. III. 241 and 50 Persei (see O 2 and 
Argelander). 

In addition to the above, a good many pairs, whose changes 
in angle and distance can be explained by the proper motion of 
the principal star, were long ago examined by Struve {Pos, Med.) 
Perhaps these should go into the list. Also the '* higher 
Bystems " of Madler wonld probably not be misplaced in it (see 
Vntersnehungen iiher die Fixstem-Systeme, 

Mr, E. CrossU^a Observatoryy 
Bermtrsidet Halifax, 
December 1876. 



On cm Oversight in the Micanique Celeste, and on the Internal 
Densities of the Planets, By George H. Darwin, M.A., 
Fellow of Trinity College, Cambridge. 

{Ckmmunioated by J, W, L, Glaiaher, F.B,8,) 

In the following paper an endeavour is made to point out an 
inconsistency, which appears to have escaped the notice of 
lAplace, in his determination of the processional constants of the 
pluiets Jupiter and Saturn, From this I have been led on to 
specnlate on the law of internal density of those planets, and of 
Man, and to make some reference to the ellipticitieB of Mercury 
tod Venus. 

I. Laplace^s Law of the Internal Density of the Planets. 

In the investigation of the fignre of the Earth, Laplace 
ttsnmed that, in molten rock, the hydrostatic pressure plus a 
constant varies as the square of the density. The result of this 
usnmption is that, after the consolidation of a planet, the density 

of any stratum of mean radius r is given by the law - sin — , where 

r a 

a is the mean radius of the surface, and and F are constants. 

Throughout the rest of this paper, besides the foregoing, the 

following notation is used : — 

o, /3, the equatoreal and polar radii ; 
c the ellipticity of the surface ; 

m the ratio of the centrifugal force of the planet's rotation 
at thd distance a to the mean pure gravity ; 




78 Mr, Dcmmnj On an Oversight in the Mecanique XXXTII. a, 

/ the ratio of the mean to the surface density ; 
G, A, the greatest and least principal moments of inertia of 
the planet ; 

P or — — — the precessional constant ; and 

M the mass. 

Other symbols will be defined as they arise. 

Then the results of the Laplacian law may be embodied in the 
following equations* : — 

3 e» e ^^' 

2. 3(/-i) / ^ ^ 

C-A«|(.-^)Mfl« (3) 

C = f{i-^^)}Ma« (4) 

m 

p ^ je* ^5; 

Now, if (following Thomson and Tait) we take for the Earth 
/= 2*1, which corresponds with d = 144°, we have 

P»i-994(.-y) (6) 

5m 



2f 



= 2562 (7) 



Hence, in any planet where the law of density is the same as in 
the Earth (i.e.,/= 2*1, Q =. 144°), we should find (7) satisfied, 
and (6) would give the precessional constant. 

In order to illustrate the Laplacian law, the following table 

has been constructed, giving the values of / and 5-!? for every 

2£ ^ 

10° of 0, with the omission of a few at the early part, which are 
rather troublesome to calculate, and are of little value. 

* Seo Thomson and Tait, Nat, Phil. §§ 824, 827. Equation (3) is indepen- 
dent of Laplace's assumption. 



Dec. 1876. OSleste^ and on the Internal Dennties of the Planets. 79 



• 



/ 
I'OOOO 


sm 

21 

2000 



90 


12159 


5m 

ac 

2*165 


10 






100 


1*2879 


2*213 


20 


1*0082 




no 


1*3827 


2*270 


30 


1 0188 




120 


1.5109 


2338 


40 


1 0341 


2*029 


130 


1*6922 


2*422 


50 


10548 


2*046 


-140 


1*9657 


2525 


60 


10817 


2*067 


150 


2*4225 


2*652 


70 


i*ii6i 


2094 


160 


3*3363 


2*813 


80 


i*i6oo 


2*126 


170 


6*0750 


3019 


90 


1*2159 


2*165 


180 


infin. 


3*290 



This table shows how ^ — increases, as the planet passes from 

2£ 

homogeneity to infinitely small surface density; £^ can never 

be less than 2, nor greater than 3*290. Although it is not strictly 
inTolved in the sabject of this paper, I may point out that the 
first column of the table may be employed to calculate the 
cllipticity of any internal stratum. I have shown elsewhere* 

tbat the ellipticity e of any stratum of mean radius —-a is given 

▼here/, refer to the surface, and/' is the value corresponding 
to 0' in the table. For example, to find the ellipticity of the 

Sttth's stratum of mean radius -La, we must take 6' = 60°, 

12 

hecauBe 6 = 144**; then from the table/' = 1*0817, and 



1*204 



(I2\* 2*ix*o8i7 
5 / ' r*o8T7"x ri 



= , when I = . 

357 297 



2. Jupiter* 8 Preeessional Constant. 

To determine the preeessional constant Laplace uses the 
followiDg argument : — " If wo suppose the densities of the strata 
of Jnpiter and the Earth, at distances proportional to the diameters 
of these planets, to be in a constant ratio to each other. . . In 
^is hypothesis, if both planets be fluid, their ellipticities will be. 



* Mutenger of Mathem.^ Not. 1876, p. 109. The notation is, howeyer, 
difierent. 



8o Mr, Darwifif On an Oversight in the Mecaihique ZXXTU. 2, 

as in [2068 A;, etc., III. v. § 43] proportional to the respectiye 
values of 0,* corresponding to each of them ; or to their ellip- 
ticities, if thej he homogeneous. If we suppose the ratio to 
obtain in their actual state, and we have seen in {2069, III. ▼. 

§ 43] that this is nearly conformable to observation, then the 

9 O — A — "R 
values of ^ will he, for each of these planets^ respectively 

proportional to the eUipticities corresponding to the ease of honuh 
geneity. These eUipticities by the same article [2068"], are as 
'10967000 to o'oo43344i."t He uses '00291193 as the Earth's 

precessional constant, and thence deduces ~" "" — = '14735, 

or in my notation P = '07368. 

By the theory of the perturbations of the Satellites, he finds 

c = '0219013; J this value does involve any assumption 

as to the law of internal density, except, I conceive, that the 
strata of equal density must be nearly spherical. § 

Then by the periodic time of the Fourth Satellite, and its 
observed distance from Jupiter, he finds m = '0987990 ; whence 
t = -07130084 

Using these values of m and e, we get ^ = 3*4642. Now 

2£ 

Laplace does not seem to have noticed that these values are not 
only incompatible with the identity of the law of internal density 
in the Earth and Jupiter j but are also incompatible with that 

form of law at all ; for, as appears from the table, ^ can never 

2£ 

be greater than 3^290. 

My attention was first drawn to the point by observing that^ 
if there wore this identity of law of density, the precessional con- 
stant of Jupiter ought to be nearly twice e , or '0438; whereas 

2 

Laplace, by a difierent method, founded on the same assumption, 
finds it to be '0737. This of course indicated that the assumption 
was untenable. 

In view of this discrepancy, it will be well to go over Laplace's 
work again by the light of later, and presumably better observa- 
tions. 

The distance of the Fourth Satellite is open to some doubt, 
but the following has seemed to me the best value attainable. 
Bessel gives the apparent distance at the planet's mean distance 
the angles as 498*8663".** 



♦ The m of this paper. 

t Bowditeh, TranB. of Mic, Oil, VIII. vii., § 23. 

X vm. ix. § 27. 

§ S» e Pratt's Fig. of Earth, Arts. 90-94. 

** Asfron, Uutersuch. Bestim. dcr Masse dcs Jupiter, Konigsberg 1842. 



Dec. 1876. Cilestey cmd on the Internal Densities of the Planets, 81 

M. Elaiser gives, as the result of a long series of his own 
obeeirations when united with those of Bessel, that the polar 
and eqaatoreal diameters of Jupiter subtend at the same distance 
35*170" and 37*563" respectively.* 

Hence the mean distance D of the Satellite is 26*5616 equa- 
toreal radii; or D = 26*5616 a ; T, the satellite's periodic time , 
is 16*68902 m. s. days, t^ Jupiter* s sidereal day is '4135 m. s. days. 
Therefore 

— '0869258 (i — •) =s !»' (i — •) suppose. 

Professor J. G. Adams informs me that M. Damoiseau 

hu recalculated the values of £ — ^, and of the masses of the 

2 

Satellites, basing his work on better observations than those 

which were available to Laplace.f He has taken, however, 

certain coefficients from Laplace, which ought to have been 

recalculated. This work has been completed by Professor Adams 

himfielf, and he has obtained the following value for c , of 

2 

which he has, with very great kindness, allowed me to make 
we, viz., 

I — =• -0216623$ 

Sabstituting then for m, we have, for the ellipticity of 
Jupiter^ — 

— + -0216623 

2 -^ , I 
< = -. =• -06241 - -2 , 

vi' ^ 16022 

1+ — 

2 

and 

m = wi' (i - •) = -o8i5oi.§ 

Laplace remarks** that the ellipticity of Jupiter may be found 

• Aitron. Nachr. 48, p. ill. 

t Titles des Satellites de Jupiter, Bnr. des liOng., Bachelior, Paris 1836. 
X The oorreeponding masses of the Satellites multiplied by 1000 are found 
byliim to be: 

•2831 13 

•232355 

•812453 
-214880 

^^ leem to bear hardly any relation to the ordinarily roceired ralues. 

i This ralue may be compared with -08163 fotind by Plana, Ast. Naeh, 
36, p. 15s. 

** VIIJ. «. § 27. 



82 Mr, Danvin, On an Oversight in the Mecanique XXXTII. 2, 

by this method with greater acenracj than by the beat obserya- 
tions. It is interesting, therefore, to observe how closely this 
yalae agrees with that of all the later observations. The follow- 
ing are the values given for the reciprocal of the ellipticity by — 
Secchi, 1606 lAst.Nach. 43, p. 142] ; Kaiser, (i) 15*36, (ii) 15*98 
[Ast, Nach, 45, p. 211] ; Bessel and £[aiser, 15*70; Bessel, 15*73; 
Secchi, 15*99 \_A8t Nach, 48, p. iii] ; Schmidt, 15*6 {^Ast. Nach. 
65, p. 102] ; Main, 16*84 \_Month, Not. Ast. 80c. 16, p. 142]. The 
redactions were in several cases made by myself. 

It is, nevertheless, a cnrions coincidence that the valne of f 
found by Laplace agreed well with the older observations of 

Struve, who found e = . [Ast. Nach, 45, p. 211.] 

Using the above value of tn, I find (following Plana *) that 
on the hypothesis of homogeneity ^= 1*1164 (compare with 
1*116515 of Plana), and therefore the homogeneous ellipticity is 

•10405. But the homogeneous ellipticity of the Earth is 

230*433 

(Plana) ; and the Earth's precessional constant is *oo3272 ; hence, 

following Laplace's method, we should have for Jupiter, 

P = * 10405 X 230*433 X '003272 
= 078451. 

Bat if Laplace's assumption as to the internal density of 
Jujpiter were justifiable, we ought to have by equation (6), 



P= 1994 f« — -j = 1-994 X 02166 



= 043. 

Thus these new values of the quantities involved leave as 
wide a discrepancy as before between the two values of P. There- 
fore, Laplace's method cannot be justified. 

3. Hie Internal Density of Jupiter. 
But this unjustifiahility may be seen in another way, for the 
new values of m and e give 5 — = 3*2646 ; and reference to equa- 

2£ 

tion (7) shows that this difiers widely from the corresponding 
value for the Earth. It is not, however, inconsistent with the 
Laplacian form of law, as was the same function when Laplace's 
values of m and c were used. In fact, I find, after some rather 

troublesome arithmetic, that ^ — = 3*2646 corresponds to 6 = 

2£ 

179® 11' 20" nearly, and to/= 68. 

• All future references to M. Plana are t<Khis paper in Astr. Xachr. 36, 
p. 154. 



Dee. 1876. CSleste, and on the Internal Densities of the Planets. 83 

Using these valnes of and /, I find by equation (5) that 
Jupiier's processional constant = 2*528 fi J = '0548; and 

this I take to be far nearer the truth than the value assigned by 
Laplace. 

On account of the uncertainty in the determination of the 
quantity m, the above valnes o£ and /can, of course, have no 
daim to precision. In fact, if following Herschel, Loomis, 

and others, we take — = 26*99835, we should find e = — 2 — , 

a 10*52 

m = '0778, and ^ — = 3*211. This last corresponds to about 

2c 

177*42', and/about 24. 

The value of the processional constant will, however, be but 

little changed, being 2*489 (e j = '0539. 

Now it seems reasonable d priori to assume that the law of 
internal density within Jupiter is of the same nature as in the 
£artb, and from that assumption it follows that the surface 
density of Jupiter is vastly less than the mean : for it must, I 
think, be admitted that numerical values can be assigned to m 
and c with some precision. 

Bat the true meaning of this result would seem to be that the 
Laplacian law of density is not exact for Jupiter, but that that 
planet must be very much denser in the centre than at the surface. 
h it not possible that Jupiter may still be in a semi-nebulous 
condition, and may consist of a dense central part with no well- 
defined bounding surface ? Does not this view accord with the 
remarkable cloudy appearance of the disk, and the remarkable 
belta? 



4. Saturn. 

The preceding method cannot be applied very satisfactorily 
to the case of Saturn, on account of the uncertainty in all the 
quantities which enter into the determination of m and e ; but 
the balance of evidence appears to me decidedly in favour of his 
surface density being far less than the mean. 

m may be best determined from the motion of Japetus, 

There seems almost complete unanimity as to his periodic 
time, and I take T ^ 79*3296 m. s. days. 

Two values are assigned for the sidereal day of Solum, viz., 
'4370 (Hansen), and '4278 (Herschel) m. s. days, the latter 
beinjf more generally accepted ; I take then t = *43o. 

There is a wide difference of opinion as to the mean distance 
D of Japetus, the estimates varying from 574 a (Jacob, Mem. Astr. 
fe''<'. vol. xxviii.) to 64'359fi (used by Herschel, Loomis, and others, 
and most generally accepted), I take D = 62 a. 



84 Mr, Darwin^ On an Oversight in the Mecanique ^TLYIL ^ 

The ellipticity seems fairly well determined at — .* 
Using these quantities in the formula 

I find 

m « '131270- '61056 8^-'Oo635 8 (-j- -14281 8«. 

(i) If all the small variations are zero, and £ = — , we get 

5^== 3-610. 

2f 

(ii) Loomis, Pract, Astron., Tables 33, 34. 
t - "437. - - 64-359. • - — . 

8<-oo7, 5-= 2*359, 8< » '01909, 

a 

then, m = '1093, ^ - a'732. 

(iii) Hind's Solar System^ pp. 103-4. 

t ■ '427s, - « 60*3436, • s= Q according to Befisel, 

a IO'2o 

8/ « —'0022, 8- a - 1*6564, 8f SB -00637, 



then, m « -1422, ^= 366. 



If wo take t = from the Greenwich Observations, ?-?? will 

bo slightly smaller. 

(iv) Captain Jacob's Madras Observations give — =57-4, and 

a 

^ ~ = — 4'6, this with c = — and all the other small variatioDB 
a II 

soro, gives m := -160 and ^ very nearly 4 J. 

No doubt other values might be assigned to ^ with equal 

2£ 

• I find the following in a p^P**" }>y Mr. Grant (Month, Not, Att, 80c. xiit 
P* I95)i when) he reduci^ ol>64^rvationi$ of apparent ellipticity to their real 

Talu«>e, Til.. Lawell -— - » Main -- . Do La Rue --j- . The mean of mil 

Hv5 92.37 iot>ii 

Beeael's obeerrationa would aeem to be - . but Mr. Hind (see below) aaeiinia 

10*20 ^ / -o 

a alighUj diil^nt ralue as Bo»«r8 rv^sult. 

Sir W. Herschel fouml ^^ ^m.v p. 7v) yyf «b\>vw \\>LV but - *-^ is also 

lo ^>o^ lo 3S4 

attributed to him on the *mo |v^ic. 



Dec 1876. Celedey and on the Internal Densities of the Planets. 85 

plaiisibility, but I think (ii) and (iv) contain extreme yalaee in 
the two directions, and the truth probably lies at some inter- 
mediate point. It is noticeable that even tne valne (ii) indicates 
a larger ratio of mean to surface density than in the Earth, 
namelj 2*809 (corresponding to 6= 155° 14'), whilst all the 
other values are far outside me limits of admissibility under the 
Laplacian law. 

1 have tried also to find m from the motion of Titan, Taking 



I find 



- - 21. T - 15-9454, < = -43, • - ^. 



m =» '13648— '1174 8^- -0195 ' ''485 8». 

CI 



If the small increments are zero, ^ — = 375 • and if the 

2e 

TarionB possible values be assigned to them, the results will be 

found to be very similar to those given above. 

The value of m assigned by Laplace is '165970,* and this^ 

together with the ellipticities — and — , gives ^ equal to 3*734 

and 4'979 respectively, either value quite incompatible with the 
lapkunan law of density. The ellipticity of the planet had appa- 
rently not been observed in his time, and the numbers used by kim 

inrolve an ellipticity of zotzj which we now know is &r too small. 

Laplace makes Saturn's processional constant - of '27934 or 

•13967 (Vni. xvii. § 37), but this value is inconsistent with any 
of those given above for m and 0. 

Taking c = — , m = *i3i3, we have £ — — = '0252. It can 
II 2 

hardly be supposed that Saturn is more nearly homogeneous than 

is the Earth, and if the law of density were the same we should, 

by (6), have P = '050. 

On the other hand, if the Laplacian law of density were to 

hold good, and if the surfisMse density were zero — of course an 

ideal casef — ^we should have by (5), 

m 
2 6_ I 

P " ' «• " 3*5505' 
or 

P a 2*5505 X '0252 =■ -064. 

• Mie, Ca, Vni. xTii. § 36. 

t It may be observed, that to be thoroughly consistent we should have in 

this ease, P » '663m » '8731, because ^— = 3*290 ; bnt the method is here 
omtj used to find the limiting value of the coefficient of • . 



86 Mr, Darwin, On an Oversight in the M^canique xxxYii. 2, 

I conceive then, that SatwnCs processional constant mast be 
very nearly equal to '06, since the former of these values is cer- 
tainly too small, whilst the latter is a little too large. 



5. Mara. 

Mars rotates in 24** 37™ 22'*6, or 1*025956 m. s. days, accord- 
ing to the elaborate observations of M. Kaiser.* His density is 
'948 of that of the Earth. f The sidereal day is '997270 m. b. 

days, and for the Earth m is — — -- ; hence for Mars. 
^ ' 289-66 

fn B -i- ^ J997270Y I 
™ -948 \ ro25956/ 28966 

- -0034409 - 5^4 

With respect to the ellipticity of the planet the most various 
estimates are given. Thus, for the reciprocal of the ellipticity 
I find, according to Loomis {Pract, Astr., Table 33) 50 ; 
Main (Month. Not Ast. 80c. xvi., p. 142) 62 ; Kaiser (Guillemin) 
Le Ciely p. 257) 118; Arago, donbtfhlly, 32; Bossel failed to 
detect ellipticity in observations at Konigsbcrg ; and lastly, firom 
observations of Dr. Winnecke, to which I shall recur below, 225 
(^Ast Nach, 48, p. 97). According to Dr. Winnecke, M. Kaiser 
doubts whether Mr. Main's result represents any corresponding 
reality. 

With an ellipticity of , we have 5- = i'93 and with the 

225 2€ 

other values of ellipticity, a very much smaller value. 

Now a reference to the table in section i will show that not 
only is even the largest of these quantities incompatible with the 
Laplacian law of density, but they are also incompatible with the 
homogeneity of the planet. We should require the planet to 
decrease in density towards the centre, or actually to be hollow ; 
and on any theory of original fluidity such a state of things is 
almost inconceivable. 

The wide discrepancy between various observations shows 
that the results are to be very little depended on ; and for the 
following reasons, I venture to think that all the above values of 
the ellipticity are almost worthless, but that Dr. Winnecke's is by 

* See a paper by M. Julius Schmidt, Ast. Nach. 82, p. 333. 
t Gnillemin, Le Ciel, p. 257. Tho other details with respect to Mara are 
giTen on the authority of M. Kaiser, and this I presume is so also. 

X Plana gives gg,„ , using slightly different data ; with Herschel's valu© 
of the density 72, m « — — - • 

220'7 



Deo. 1876. GSUstey and on the Internal Densities of the Flcunets. 87 

far the nearest to the truth. He gives* as the eqoatoreal and 
polar apparent diameters, ()"'22'j and 9''' 186, subject to mean 
errors of '045" and '032" respectively. 

From these measurements I find that the probable error of the 
ratio of the axes is '0050441. The ratio itself is in decimals 
'09 5 5564, and therefore the ratio of the axes is '9955564 
^'0050441. That is to say, it is an even chance that the ratio of 
the axes lies between the i'ooo6 and '990512. In other words, 
it results from Dr. Winnecke's observations that it is an even 
chance that the figure of Mars lies between a prolate spheroid, with 

an ellipticity of , and an oblate one with an ellipticity of 

; the observed values give an ellipticitj of 



105 ° * "^ 225* 

Dr. Winnecke himself says, " Es sprechen diese Messungen 
entschieden gegen eine Abplattung des MarSy die fiir das Berliner 
Instrument messbar ware." 

Now the telescope shows that Mars has an external physical 
constitution exceedingly like that of the Earth, and therefore 
there is a strong probability that its internal structure is some- 
ivhat ihe same. Seeing then that the observations of the best ob- 
servers permit such very wide limits of error, and that the value 
of m can be assigned with some precision, I submit that there is 
a far better chance of being near the truth in trusting to indirect 
evidence than to direct observation, for the determination of the 
ellipticity. Assuming then that the law of internal density is the 

same as in the Earth, I find an ellipticity of — -, and this, I 

298 

Tenture to think, is nearer the truth than any of the above- 
quoted values derived from observation. 

6. Mercury, Venus. 

M. Plana assigns as the values of m for these planets, 
and respectively ; and following the arguments 



325-82 251-54 

used in the case of Mars (although they have not here equal 

force), we should assign to Metxury an ellipticity of about 

and to Venus of about 



330 260 

7. Conclusion, 

The results arrived at may be summed up as follow : — 
The values assigned by Laplace to the precessional constants 
of Jupiter and Saium cannot be maintained ; and the objections 

* A$t. Nach. 48, p. 97. The observatioDs are said tx> be reduced for 
*' Phase und Refraction," but I do not see it expressly stated that they are cor- 
r«cied for the Earth's Martian declination. 



88 Mr. Dartmn, On Overnght in Mecanique Celeste ete. xxxvn. 2, 

to them remaiii eqaallj strong when later observations are 
consulted. 

Professor Adams's calcnlation of e gi^es, as the ellipticity 

of Jupiter, —. — . 

l6*02 

The Burisuce density of JxvpUer is &r less than the mean, and 
he may perhaps still be in a semi-nebnlous condition. 

There is a considerable probability that the like is true of 
Saturn. 

The value of Jupiter's precessional constant is about '0548 ; 
and that of Saturn probably about *o6. No dependence is to be 
placed on the observations of the ellipticity of Mars, because of 
their wide limits of error. Indirect evidence of the ellipticity 
seems safer, and we are thereby led to assign to him an ellipticify 

^^ — -. In the cases of Mercury and Venus, we have only indirect 

o^idence to rely on, and these eUipticities are probably about 
and 



330 260 

In conclusion, I must add that if in any case I have under- 
rated or neglected the work of important observers, or have over- 
rated the worth of other observations, my excuse must be mj 
previous slight acquaintance with observational astronomy. 

Postscript. — The method of this paper may perhaps give 
some idea of the amount of difference which might be expected 
to be found between the apparent equatoreal and polar diameters 
of the Sun. 

To find m, the Earth may be treated as a solar satellite, and 

the same formula as before applied. -=- is here the Sun's mean 

apparent radius (which I take as 961 "'82) in circular measure. 

T = 365*2569 m. s. days. 

t, according to Carrington, is 25*38 m. s. days. 
But Mr. Christie (to whom I owe my thanks for his help in this 
matter) informs me that the true period may perhaps be 26 or 
27 days. The following results are therefore given in duplicate ; 
in those marked with an accent t is taken as 27. 

Then m = '00002100, or m' = '00001829. 

If the law of internal density were the same as in the Earth, 
we should have, 

€ = -00002048, or e' = '00001784. 

These correspond to differences of apparent diameter of 
•0394" and '0343" respectively. If the Laplacian law of density 
were to hold good, and if the surface density were zero, we should 
have, £ = '00001596, or i' = '00001390, which correspond to 
differences of '0307" and '0267" respectively. 

Mr. Christie informs me that the probable error in the d< 



Dec. 1876. Mr, Neisony On Point of Max. Brightness on Venus, 89 

termination of the Snn's apparent diameter is not less than 0*1'', 
and it appears that the observed difference of diameters is also 
o-i". 

May we not conclude that the difference of the apparent 
diameters is probably less than '04", but perhaps greater than 
-03" ? 



Note on the Relative Space-penetrating Power of the PuVcowa i ^-inch 
Refractor and Mn LasseUVs ^-foot Reflector, By M. Otto Struve. 

In his paper ** On the Relative Power of Achromatic and 
Reflecting Telescopes" {Monthly Notices^ vol. xxxvi. pp. 305-309) 
Dr. Robinson makes the following statement : — 

" 2, Otto Struve thought that the Pulkowa Achromatic of ' 
iS-inches was equal to Lassell's 24-iTich Newtonian (not his 
4-feet, as supposed by M. Radau) : nothing definite can be built 
on this." 

I feel sure, if Dr. Robinson had read my paper, " Ueber das 

von Herm W. Lassell in Malta aufgestellte Spiegelteleskop," 

published in the beginning of 1864 in the Bulletin ae VAcademie 

de St,-Petershourgy he would have considerably modified his 

words, and perhaps also his views. In fact, M. Radau has been 

quite correct in his statement. I wrote the above-mentioned 

paper immediately ader having visited my honoured Mend Mr. 

Lassell at Malta. Together with some other results derived from 

practical experience, I have given there, in extenso, the comparison 

of the ultima visibilia in the nebula of Orion^ observed at 

Pnlkowa by Dr. Winnecke, simultaneously with me, at Malta. 

Tlie result of this comparison is expressed in the following 

terms: — "The preceding comparison of almost simultaneous 

obsenrations made at Malta and Pulkowa proves evidently that 

tlie space-penetrating power of Lassell's new (4-feet) instrument 

can hardly be estimated superior to that of ours (the Pulkowa 

>S*inch) refractor ; especially if we consider that at Pulkowa 

the nebula of Orion has been observed at a height of only 25°, 

^hile at Malta the observations were made at the height of 49°." 

I beg leave to add that in 1863, as a great many comparisons 

"^ al^ut that time have proved, my eye vras still quite of the 

"Mne strength with that of Dr. Winnecke. 

^hwa, 1876, November, 



On the Position of the Point of Maximum Brightness on Venus, 

By E. Neison, Esq. 

Supposing Venus to reflect the solar rays from a dead or un- 
polished sumce, the intensity of illumination of the surface 
^ any point P will be proportional to the cosine of the zenith 

o 



90 Mr, Chrtstie^ Note on the Oradaiion xxxm. a, 

difltanoe of the San (=2) at that point. Then from a known 
optical principle, the i^parent brightness of the snrfaoe at P as 
seen from the Earth will be proportional to the real illomination. 
Consequentlj, the apparent brightness B of any point on Venus 
as seen from the Earth will be 

B « A cos r. 

The point where the apparent brightness is greatest will be 
therefore that where the Son is in the zenith. 

Conseqnentlj, when Venus is crescent, or less than one half of 
the illnminated hemisphere of Venus is visible, the limb of the 
planet will be the brightest portion. This is what the observations 
of Gapt. Noble (MotUhly Notices, vol. xxrv. p. 350) have alreadj 
indicated. When, however, the planet is gibbons, so that mora 
than half the illnminated hemisphere can be seen; then the point 
of maximum illumination will be within the limb. Under these 
conditions, in fact, the region of maximum brightness will be au 
eUipse of great eccentricity. 

This is in accord with the observations of Mr. Chnstia, 00m- 
municated to the Society in November 1876. 

These two series of observations are not therefore, discordant, 
as might be supposed, and neither confirm the hypothesis that 
the solar rays are specularly reflected from the surfebce of Venut, 



Note on the Gradation of Light on the Disk of Venue. 
By W. H. M. Christie, Esq. 

Some months ago Mr. Brett pointed out that there was a 
gradation of brightness towards the limb of Venus as well as, in 
a more marked degree, towards the terminator, and he con- 
sidered that this was due to specular reflexion modified by large 
atmospheric dififusion. As Venus was then becoming orescenU 
shaped, and therefore unfavourably situated for showing anj 
effect of specular reflexion, I had no opportunity of testing tfaie 
point till after inferior conjunction. When the planet became 
gibbous again, I examined the disk on several occasions in the 
forenoon with the direct- vision polarising eyepiece, described in 
the Monthly Notices for last January, applied to the Great 
Equatoreal of the Greenwich Observatory, and was thus enabled to 
reduce the brightness very gradually to the point of total disap- 
pearance. On October 1 2 the disk was reduced, on turning the 
Nicol prism, to au oblong patch, the edge of which was distant 
about one-sixth of the diameter of Venus from the limb, special 
attention being directed to this point. Afterwards, on Novem- 
ber 28 and December 6, under more favourable circumstanceSy 
four distinct phases were remarked, corresponding to different 
readings of the position-circle attached to the Nicol, 9" 
indicating four different degrees of brightness : 



Dec 1876. of Light on the Dish of Venui. 91 

(a) At the first pkase the limb was jast beginning to fade, the 
disk being then gibbons, though a small portion near the ter- 
minator had, as &r as I could judge, already disappeared. 

(b) The next phase was an oblong patch, from two-thirds to 
three-quarters of the planet's diameter in length, in the direction 
of the line of cusps, and about one-third as broad as it was long. 

(c) On turning the Niool further, the ends of this patch dis- 
appeared, and a nebulous spot, about one-third of the diameter 
of Venus, and condensed towards the centre, was seen. 

(d) Finally, just before total disappearance, the disk was 
reduced to a nearly stellar point from one-sixth to one- tenth of 
the original diameter, and surrounded by an extremely faint haze, 
which was occasionally invisible, leaving nothing but a minute 
point of light to be seen. The appearance was exactly*that of the 
nucleus of a smaU comet, or of a nebulous star. By the help of 
a pointer in the field of view, the position of this stellar point 
was found to be about the middle of the visible disk. 

From several sets of closely accordant readings of the position- 
circle, taken with the eyepiece in various positions, the angles 
for the Nicol measured from the position for which its plane of 
polarisation is perpendicular, to the plane of reflexion in the eye- 
piece, were found as foUows for the respective phases : — 

(a) 300 (h) 240 (c) i3« (d) ii«» 

Since the intensities of light transmitted by the Nicd are as the 
aquares of the sines of the above angles, we get, taking the 
£Euntest portion of phase a as standard: — ^brightness of 6 = 1*5, 
of e=4'8, of (2= 7*0. So that it would appear that the centnd 
portion of the disk is about seven times as bright as the part 
near the limb. It may be thought strange that so great a 
difference in brightness should not be more noticeable, but it 
would seem that a highly-trained eye is required to detect a 
gradation in bright objects, though when the brightness is 
reduced nearly to the vanishing point, there is no difficulty in 
seeing it. In the polarising eyepiece the light is reduced in the 
first instance to about i -3000th part by the three reflexions, and 
with the Nicol at the reading for pha^ d it is further reduced 
to one-thirtieth of this amount, or i-90,oootb of the original 
brightness. Though the extinction method of photometry is 
liable to large error from variation in the sensitiveness of the 
eye, it may be trusted for comparative results, where, as in this 
case, there is an extremely fskint background of scattered dayh'ght, 
which gives a sort of standard for comparison. 

Whatever uncertainty there may be in the actual values 
found for the brightness, there can, I think, be no doubt of the 
fiurt of a considerable gradation of light frt)m a central, or nearly 
central spot ; and it seems difficult to explain this on any other 
hypothesis than that of specular reflexion modified by atmo- 
spheric diffusion. 

1876, December 7. 



92 Trof, Cojfley, On Spheroidal Trigonometry, xxxvn. 2. 

On Spheroidal Trigonometry. By Prof. Cayley. 

The fundamental formnlee of Spheroidal Trigonometry are 
those which belong to a right-angled triangle PSBg, where P is 
the pole, PS, PS^ arcs of meridian, and 2SSo a geodesic line 
cutting the meridian PS at a given angle, and the meridian 
PSo at right angles. We consider a spherical triangle PSS^, 



Sides 


PS. 


PS.. 


SS. -7. 


7.. 


». 


Angles 


s.. 


8, 


P =90'. 


». 


I, 



where y is the reduced colatitude of the point S on the spheroid 
(and thence also y^ the reduced colatitude of S^) and the 
azimuth of the geodesic SS^, or angle at which this cuts, the 
meridian SP ; and then if S be the length of the geodesic SS^ 
measured as a circular arc, radius := Earth's equatoreal radius, 
and L be the angle SPSoi S, L differ from tlu^ corresponding 
spherical quantities «, I by terms involving the ezcentricily of the 
spheroid, viz. calling this e and writing 

, « cos 7a 



'v^i— c'8in*7o 



then (see Hansen's Geoddtische Untersuchungen, Abh. der K, Sachs. 
OeselL, t. viii. (1865) pp. 15 and 23, but using the foregoing 
notation) we have, to terms of the sixth order in e, 

\ 4 64 256 / 



+ (0 



\S 32 1024 / 

+ 1 — 7 *• + -^ ^1 sin AS 
\256 1024 / ^ 



+ A* sin 6« : 

3072 



and 

-(~T^+ — A:* I sin 2* 
\i6 32 / 

+ 2^6** sin 4*} 
which are the formulas in question. 



MONTHLY NOTICES 

or THB 

ROrAL ASTRONOMICAL SOCIETY. 

VolXXXVIL January 12, i8yy. No. 3. 

William Huggins, Esq., F.R.S., President, in the Chair. 

Bobert John Baillie, Esq., 10 Bolton Place, Carlisle ; 

H. Vere Barclay, Esq,, 6 Disraeli Terrace, Putney ; 

Ber. Daniel Datton, Sandbach, Cheshire ; 

Samuel Heywood, Esq., 171 Stanhope Street, Hampstead 

|U>ad; 
Louis Stromeyer Little, Esq., M.D., B.A., 18 Park Street, 

Ghrosvenor Square ; 
Bobert Pearce, Esq., Church Court Chambers, Old Jewry ; 
Commander William James Lloyd Wharton, H.M. Surveying 

Ship "Fawn;" 
Jesse Young, Esq., Stibbington House, Wantsford, 

trere 1)alloted for and duly elected Fellows of the Society. 



theory cf (he HorizonUil Photoheliograph, inoluding its appUcation 
io the deterrnincUion of the Solar Parallax by mea/ns of Tramita 
cf Venus, By Professor William Harkness, U. S. Navy. 
(Abstract.) 

(Cammumeated by the Astronomer Bof/al.) 

THe term " Horizontal Photoheliograph " is used to designate 
tliat form of photoheliog^ph which, it is believed, was first 
employed by the late Professor Winlock, and which consists 
enent^y of a fixed telescope, whose optical axis is accurately 
horizontal and in the meridian, and whose objective is directed 
towards the same side of the zenith as the elevated pole ; the 
Son's r^s bein^ reflected into the telescope by a suitable helio- 
itat The sensitive plate for the reception of the photographic 
iisage is, of course, situated at the chemical focus of the telescope, 



94 T^fof, HarknesSy Horizmital Photoheliograph etc, XXXYIL 3, 

the plane of the plate being perpendicular to, and its centre 
coinciding with, the optical axis of the telescope. 

The heliostat mirror consists of a piece of highly polished (Imt 
nnsilvered) glass, whose two surfaces make an angle of about 
siztj minutes with each other. The front surface is worked as 
truly plane as possible, and serves to reflect the solar rays thzoagh 
the object-glass to the photographic plate. In working the back 
surface, no particular pains are taken ; and, on account of its 
inclination to the front surface, any light reflected from it is 
thrown entirely away from the photographic plate. The object- 
glass is corrected for the chemical, and not for the visual rays. 
The distance between the object-glass and mirror is made as small 
as possible, consistently with keeping the latter clear of the 
shadow of the former. The sensitive surface of the photographio 
plate faces the object-glass, while the rays from the Sun are 
reflected by the mirror through the object-glass, and after 
traversing the reticule, they form an image upon the photo- 
graphic plate. 

The reticule consists of a system of squares, formed by the 

intersection of two systems of very flne straight lines, whion are 

drawn upon one side of, and respectively parallel to, the edges of 

a thin square plate of piano-parallel glass. In each of these linear 

systems the number of lines is odd, and the middle line is drawn 

through the centre of the plate. This reticule is fixed with its 

ruled surface toward, parallel to, and two or three millemeters 

distant from. Hike sensitive surface of the photographic plate. 

Moreover, one of the two systems of lines is set as nearly as 

possible vertical, and its inclination is accurately determined; 

and, to render assurance doubly sure, a plumb-line, consisting of 

a silver wire about 0*05 of a millemeter in diameter, is suspended 

between the reticule and the photographic plate, in such a position 

that it may hang freely, and at the same time be very pearly in 

the vertical plane passing through the centres of the reticule and 

object-glass. As the light from the object-glass traverses the 

reticule before it reaches the photographic plate, the shadow, both 

of the reticule and of plumb-line, is impressed upon every picture 

taken with the apparatus; and thus three dlflerent ends are 

gained : First, by comparing the squares of the reticule with 

the corresponding ones upon the picture, everything relating to 

the shrinkage of the collodion can be determined ; secondly, the 

impression of the plumb-line, and also that of the vertical 

lines, furnishes upon each picture a fixed direction from which 

to measure angles of position ; and, thirdly, the intersection of 

the middle vertical with the middle horizontal line furnishes 

a fixed point, which in the paper is designated as the centre 

of the plate. To determine the zenith distance and azimuth 

of this point, it is necessary to measure the zenith distance 

and azimuth of the corresponding point of the reticule, as 

seen from the second principal point of the object-glass. 

For that purpose, the mirror is temporarily removed, and a 



Jan. 1877. Mr, Knott, Micrometrical Meastures of Double Stars, 95 

transit instiniment is sefc np in fronfc of the object-glass in pro- 
longation of its axis. The object-glass thus becomes a collimator 
to the transit instrument, through the eyepiece of which the lines 
of the reticole maj be observed as if they were at an infinite 
distance. It should be remarked, however, that as the reticule is 
iliehtly inside the visual focus of the object-glass, it is not gene- 
nOjr possible to obtain perfectly distinct vision of its lines and of 
the wires of the transit at the same time. This difficulty is 
obviated by marking the intersection of the middle vertical and 
middle horizontal lines of the reticule in such a distinct manner^ 
that the slight maladjustment of focus does not prevent it from 
being seen. Then, by means of the transit, the reticule is 
adjusted so that the point in question is very approximately in 
the meridian, and at a zenith distance of ninefy degrees. Finally, 
the exact azimuth and zenith distance of the point are measured. 
The remainder of Professor Harkness's paper, which will pro- 
Ubly be g^ven in extenso in the Memoirs of the Society, is occupied 
with a full and detailed explanation, with diagrams, of the prin- 
ciple of the instrument, and of the methods of measurement of the 
fMographs. 



Kcrometrical Meastures of Double Stars, By Qsorge Knott. 

(Abstract).* 

I have the honour of presenting to the Boyal Astronomical 
Society a short series of Micrometrical Measures of Double Stars, 
**ken between the years i860 and 1873, at my former residence, 
Woodcrofb, Cuckfield. 

The Observatory, detached at some little distance from the 
^Qse, and commanding a good horizon view, stood at an eleva- 
tion above the sea level of about 370 feet, and in the approximate 
position, latitude 51° o' 41" North, longitude o'' o"* 34" Wesfc. 

The Equatoreal has an object-glass of 7^-inches clear aper- 
ture and iio^inches focal length, by Messrs. Alvan Clark and 
Sons of Boston, U.S.A., and is a fine specimen of the makers' 
>kilL It was formerly in the possession of the Bev. W. B. 
Bawes. 

The filar, or parallel- wire, micrometer, employed in the fol'^ 
Wing measures, was made for me by the late Mr. Dollond. It 
has a position-circle of 3^inches diameter, reading, by two ver- 
niers, to tenths of a degree, and the angle of position is taken by 
placing the two stars under observation centrally parallel between 
two thick wires, about 13'' apart. At right angles to the posi- 
tun-wires are the webs for distance-measures, of which two, one 

' The Paper will probably appoar in extenso in the Memoirs of the 
Sodety.— Ed. 

H 2 



96 Mr. Hind, On the Orbit of a Oentcmri, XXXVIL ^ 

fine and the other coarse (the latter for measures of &ant objectSy 
bat rarely used), are carried hj each screw. 

The screw-heads, divided to 100 parts, are of nearly two inches 
diameter, and are fitted with bolts, so that either web may be 
fixed as zero- wire, while the other is nsed in making the measiiTeB. 
There is a battery of seven eye-pieces, with magnifying powers 
from 1 1 5 to 5 1 5, and, by the nse of an achromatic concave Barlow- 
lens, the magiufying power may be increased in the proportion of 
about 2*25 to I. The micrometer is also fitted with a convenient 
slipping-piece. The value of one revolution of the screw is 
i8"'2949, and with the Barlow-lens, 8'''0765. 

In reducing the observations, the arithmetical mean is taken 
as the mean for the night. To each individual measure a num.ber 
is assigrned (1-9) expressive of its estimated worth, and the sum 
of these numbers is taken as the weight of the set, which is thus 
a function of the number of observations and of the estimated 
value of each measure. In forming the " Mean results " (or mean 
of several nights' measures), this number is introduced as the 
comhviuUion weight. 

Being interested in the observation of Variable Stars, I found it 
convenient to adopt Mr. Pogson's standard scale, or Aigelander^s 
scale extended to the lower magnitudes by the adopted Hghi-ratio 
2*512. (Monthly Notices, vol. xvii. p. 15.) The numbers expressing 
the magnitudes will be found therefore to lie generally between 
those of 2 on the one hand, and that of H. and Sm. on the other, 
the difference being more marked in the lower magnitudes. Al- 
though, for convenience, the magnitudes are expressed decimally^ 
they must not be regarded as making any pretensions to very dose 
accuracy. 

CktckfiOd, 
1877, January 11. 



On the Orbit of a Oentcmri, By J. R. Hind. 

Having been lately favoured by Lord Lindsay with the results 
of two sets of measures of the angle of position of a Centauri made 
with the heliometer at the Mauritius in November 1874, during 
his Lordship's expedition for the observation of the transit of 
Venus, 1 have attempted a further approximation to the elements 
of this most interesting binary. 

I employed the last orbit by Mr. Eyre B. Powell, of Madraa^ 
in the formation of equations of condition, for the epochs of the 
most reliable mean results, depending on the measures of Sir John 
Herschel, Captain Jacob, Mr. Powell, and Lord Lindsay, at the 
same time admitting the angle for 1752*2 g^ven by Lacaille'sBiglii 



Jan. 1877. ^r* Hind, On the Orbit of a CerUanri. 97 

Aflcenfiion and Declination. The elements obtained bj the solution 
of tJie equations are as follow : — 



Peri-astron passage 


1874-85: 


Node 


t 
21 48*0 


Node to peri-astron on orbit 


59 321 


Inclination 


82 i8'4 


Angle of eccentricity 


41 515 


or e » ©•6673 




Semi-axis major 


It 
21797 


Period of revolntion 


yn. 
85042 



The following is the comparison with observations :— 

Portion (0-0). Dittanoe (0-0). 

O It 

lieaiBe 1752*2 -08 -47 

Mmdo 1825-0 -4'o +0*2 

Johnson 1830*0 —2*1 +0*2 

0^ 18330 -2*9 +o*i 

Hanchel 1836*00 —2*6 

„ 1836-06 ... -0*23 

Cape 1840*0 +3*9 — 3*22 

Jacob 184675 —2*7 —107 

It 1848*02 —2*6 —0*28 

>i 1850*83 -2*1 —0*32 

ft 1852*23 —2*7 —0*15 

n 1856-27 +1*6 —0*16 

» i857'i5 +i*o +0*03 

^***«fl 1859*38 +0*9 —0*98 

>i 1860*11 +1*0 —0*18 

It 1861*05 +1*0 +o*o6 

»f 1862*21 -07 +0-1 1 

It 186308 -07 +029 

« 1863*11 — 4"9 —0*34 Position preferred 



n 1870*10 —30 +023 

liwiwj 1874*85 +04 



by Powell to last 



It will be remarked fhat Lord Tiind say's measures fall 
wictly at the computed time of nearest wpproach of the com- 
ponent stars in the real oibit. Probably a somewhat closer 



gS. Mr. Marih, Bplemerisfor Sateltiies of Vramu. xtxvd; J, 

representation of the observed angles and distances might be 
obtained by repeating the process npon which the above elementB 
were dednced, but I defer anj farther computation in the hope of 
soon receiving measures made after the passage of the peri-astron. 
Lord Idnasaj's epoch, as used above, is, 



187485 



,0. 



34"i7 



If, for the annual parallax, a mean of Henderson's value, as 
corrected bj Peters, and that of Moesta, be taken, giving 
o"*928, we find the mass of this system = 179 x 0's mass, and 
for the semi-axis major of the orbit 23*49. 



Ephemerisfar Determining the Positions of (he Satellites of Uranus^ 187^ 

By A. Marth, Esq. 

{Communicated by A. C. Ranyard, Esq.) 



Greenw. 
Koon. 
X877. 

Jan. 25 


P 

l( 

10*48 I 


Arid. 
>g a log 6 

181 1 0*7569 


rmhrid. 
log a log b 

1-3251 09009 


Titania. 
log a log 6 

1*5400 III58 


Oberon. 
log a 

1*6662 


log» 
1*242 


30 


1041 


I817 


7613 


•3257 


•9053 


•5406 


*I204 


•6668 


*24£ 


Feb. 4 


IO-34 


I82I 


•7656 


•3261 


•9096 


•5410 


•1245 


•6672 


'2S/C 


9 


10*27 


1823 


•7697 


•3263 


•9137 


•5412 


1286 


•6674 


'2S4 


14 


10*21 


1823 


7736 


•3263 


•9176 


•5412 


•1325 


•6674 


•2s€ 


19 


10*14 


1822 


7772 


•3262 


•9212 


•541 1 


•I36I 


*6673 


•26= 


24 


1007 


-I818 


7806 


•3258 


*9246 


•5407 


•1395 


•6669 


•26 j 


Mar. I 


IQ-OI 


•I8I2 


7836 


•3252 


•9276 


*540i 


•1425 


•6663' 


•26^ 


6 


995 


•1804 


7S62 


•3244 


•9302 


•5393 


•I45I 


•6655' 


•27: 


II 


989 


1795 


788s 


•3235 


•9325 


•5384 


•1474 


*6646 


'271 


16 


9-83 ' 


1784 


7903 


•3224 


•9343 


•5373 


•1492 


•6635 


27s 


21 


978 ■ 


1772 


7918 


•3212 


•9358 


•5361 


•1507 


*6623 


•276 


26 


973 ' 


•1758 


7928 


•3198 


•9368 


•5347 


•I5I7 


•6609 


•277< 


31 


969 


1743 


7934 


•3183 


•9374 


•5332 


•1523 


•6594 


.2781 


Apr. 5 


966 


•1727 


7935 


•3>67 


•9375 


•5316 


•1524 


•6578 


•2781 


10 


9-63 


1710 


7932 


•3150 


•9372 


•5299 


•I52I 


6561 


•2' 


15 


9-61 


1692 


7925 


•3132 


•9365 


•5281 


*I5I4 


•6543 


•2 


20 


960 


•1673 


7913 


•3"3 


•9353 


•5262 


•1502 


•6524 


•2 


25 


959 


•1654 


•7896 


•3094 


•9337 


•5243 


•i486 


•6505 


•a 


30 


959 


•1635 


•7878 


•3075 


•9318 


•5224 


•1467 


6486 


•2 


May 5 


960 I 


1615 


07854 


1-3055 


09294 


1*5204 


11443 


16466 


V2 



Jan. 1877. Mr. Maaihy Ephemerisfor SateUites of Uramu, 99 

a and h are the major and minor semi-axes of the apparent orbits 
of the satellites, expressed in seconds of arc ; jp^ is the position- 
angle of the major axes. The longitudes 01 of the satellites in 
their orbits, recKoned from the points of their greatest northern 
elongations, are the following : — 





Arid. 


UmbrieL 


TitoniA. 


OberoD* 


Sia. 


* 


diff. 


* 


diff. 


* 


diff. 


* 


diff. 


^25 


168*^28 



714-16 


330-37 



434-32 


19^65 



206*72 


24^*04 



13367 


30 


162*44 


•15 


4469 


•31 


22637 


72 


21-71 


•66 


¥cfau 4 


156-59 


•15 


1 1900 


•31 


7309 


72 


155*37 


•66 


9 


15074 


•14 


193*31 


•31 


279-81 


•72 


289-03 


•66 


14 


144-88 


•13 


267*62 


•30 


126-53 


•72 


62*69 


•66 


19 


139-01 


•13 


341-92 


•30 


33325 


•72 


196-35 


•66 


24 


I3314 




5622 




179-97 




320-01 




«^ 




-12 




•30 


■ 


•72 




•66 


Kar. I 


12726 




13052 




2669 




103-67 




m 




•12 




•30 


f 


71 




•66 


6 


121-38 


-12 


204-82 


•29 


23340 


•72 


237-33 


•66 


II 


115-50 


-12 


279-11 


•30 


80-12 


72 


10*99 


•66 


16 


10962 


-II 


353-41 


•29 


28684 


•72 


144-65 


•67 


« 


10373 


-10 


6770 


•30 


133-56 


-72 


278*32 


-66 


26 


9783 




142-00 




340-28 




51*98 








•II 




•29 




-72 




-67 


31 


9194 




21629 




18700 




185-65 




^l 




•11 




•30 




•73 




.67 


86-05 




290*59 




33*73 




3*9-32 








•II 


• 


•29 




-72 




•68 


10 


8016 


•10 


4-88 


•30 


240-45 


•73 


93-00 


-67 


>S 


7426 




79-18 




87-18 




22667 








•II 




•30 




-73 




•68 


' 20 


68-37 


•II 


153-48 


-30 


29391 


•74 


0-35 


-69 


25 


62-48 


•II 


227-78 


•31 


140*65 


•74 


13404 


-68 


30 


5659 




302-09 




347-39 




26772 




«*r 5 




714-12 




434-30 




20674 




133*69 


50-71 




1639 




194-13 




41*41 





These yalnes must be interpolated for the times for which 
the position of the Satellites are required. The angles of position 
p tod distances « are then found by means of the equations — 

J sin (i>o— p) ^ ^ Bin ctf. 
$ cos {jj^o^f) "> a CO0 «. 



loo Mr, Marthf i^Jtemeris for SateUUes of Uramu, xxxm. 3, 

The interpolation of the yalnes of to may be facilitated by the 
following tables, which give the motion of la for every even hoar 
of the five days' interval: — 







Ariel, d 


iff. = 7i4®-i2. 






b 



o« 
0*00 


I* 
142*82 


2* 
285*65 


3* 
68-47 


4* 

211^50 


2 


ii'90 


154*73 


297*55 


80-37 


223*20 


4 


23*80 


16663 


30945 


92*28 


235-10 


6 


3571 


178-53 


321-35 


104*18 


247*00 


8 


47-61 


190*43 


33325 


Ii6x>8 


258-90 


10 


59*51 


202-33 


345*16 


127-98 


270*81 


12 


71-41 


214-24 


35706 


139*88 


282*71 


14 


83*31 


226-14 


896 


151*79 


294-61 


16 


95*22 


238-04 


20-86 


163*69 


3o6rsi 


18 


107-12 


24994 


32-77 


175*59 


318*41 


20 


119-02 


261*84 


44.67 


187-49 


330*3a 


22 


130-92 


27375 


56*57 


199*39 


342*22 



142*82 285*65 68'47 211*30 354*12 



Umbriel, diff. = 434^*28. 





o« 


I* 


2« 


3* 


4* 


b 




















o*oo 


86-86 


173-71 


260*57 


34r42 


2 


724 


9409 


180-95 


267*81 


354*66 


4 


14*48 


101-33 


188*19 


275*04 


1-90 


6 


2171 


10857 


195-43 


282-28 


914 


8 


2895 


115-81 


20266 


289*52 


16-38 


10 


3619 


12305 


20990 


396-76 


23-61 


12 


4343 


130-28 


217*14 


30400 


3085 


14 


5067 


137-52 


22438 


3ii'23 


38-09 


16 


57*90 


144-76 


231-62 


318-47 


45-33 


18 


6514 


15200 


23885 


325-71 


52-57 


20 


7238 


159-24 


24609 


33295 


59*80 


22 


7962 


166-47 


2S333 


340-19 


67*04 



24 86*86 173-71 260-57 34742 74.JS 



Jan. 1877. Mr, Marth, Eph&meriefor 8(UeUUeB i^ Uxanus. loi 







TUatUa, diff. 


a 206^-70. 


» 






0* 




I* 




2* 




3* 








otx> 


41-34 


82-68 


124*02 


165^ 




345 


44-79 


86-13 


12747 


i68-8i 




6-89 


48*23 


89-57 


130*91 


172'25 




10-34 


51-68 


93*02 


134-36 


175*70 




1378 


55-12 


9646 


137*80 


179-14 


10 


1723 


58-57 


99-91 


14125 


182-59 


13 


20-67 


62*01 


103-35 


144*69 


186-03 


M 


24*12 


65-46 


106-80 


148-14 


189-48 


16 


2756 


68-90 


110*24 


151-58 


192*92 


18 


31*01 


72-35 


1 1369 


15503 


19637 


90 


34-45 


75-79 


117-13 


158*47 


199-81 


2S 


37-90 


79-24 


120-58 


16192 


203-26 



41*34 82-68 124*02 165-36 206-70 



Oberan, 61S. - 133^*68. 



V 


o« 


I* 


2* 


3* 


4* 


1 




















otx> 


26*74 


53-47 


80*21 


106*94 


3 


2*23 


2896 


55-70 


82*44 


I09'i7 


4 


4-46 


3119 


57-93 


84-66 


111*40 


6 


6-68 


33-42 


60-16 


86*89 


113*63 


8 


8*91 


35*65 


62-38 


89*13 


115*86 


10 


11-14 


37*88 


64*61 


91-35 


118*08 


13 


13-37 


40*10 


66*84 


93*58 


120*31 


H 


1560 


42*33 


69*07 


95*80 


122*54 


16 


17*82 


44*56 


71-30 


9803 


124*77 


18 


20-05 


46-79 


73*52 


100*26 


127*00 


90 


22*28 


49*02 


75*75 


102*49 


129*22 


23 


2451 


5124 


7798 


10472 


131-45 



26*74 53*47 8021 106-94 133*68 









102 Mr, PlimivAffr,' On Conjunction of Venus and X (}em, xxxVn. 3, 
• * • • 






• • 



• - • • 

• • .' On the Conjunction of Venus a/nd X Oeminorufn, 

By John I. Plummer. 

In a late number of the Monthly Notices (vol. xxxvi. p. 340) Mr. 
Dankin has called attention to the proposal of Dr. Kroger, that 
astronomers in either jbemisphere should avail themselves of the 
near approach of Venus to the bright star X Geminorum, at a time 
when the planet was but little distant from the Earth, with the 
view of determining the solar parallax. It may, therefore, be of 
interest to the Fellows of the Society to record the degree of suc- 
cess that has attended the observations at the Orwell OBservatory. 
The plan which it was proposed to pursue on the occasion, was 
to measure differences of declination of the planet and star, com- 
mencing as soon as Venus had attained an altitude 01 20°, to be 
continued so long as circumstances would permit, since with the 
large aperture at my command (10 inches), no difficulty would' 
be experienced in following up the observations to the time of 
actual conjunction in Bight Ascension. Five comparisons of each- 
limb of the planet with the star were to be made with a parallel- 
wire micrometer (power 315) alternately, and it was confidently 
expected that the probable error of the mean of each set would 
not exceed xxs^^i of a second of arc. Such a series would have 
been useful if corresponding observations had been made at any 
position in the so.uthem hemisphere, and failing a preconcerted 
arrangement with a southern station, was the most satisfactory' 
scheme that suggested itself to my mind. 

Unhappily it was discovered on the morning of August 18,- 
that the definition of the planet and star was not sufficiently 
sharp for the desired degree of accuracy to be ensured, and was 
at times so indifferent that I was doubtful whether measures 
avowedly so delicate ought not to be discontinued. They were,* 
however, persevered in until 18^ 46™ G.M.T., when cirrus cloud 
overspread the sky, obliterating both objects for several hours. 
By this time 10 sete of 5 comparisons each had been obtained, and, . 
although these may not folly serve the end for which they were 
undertaken, they quite unexpectedly throw light upon a questi6n 
to which I have always attached some interest. 

The following is a comparison of the observations with 
the Ephemeris of the Nautical AlmanaCy which has been made in 
order to test the reliability of the individual sets, assuming, for 
the purposes of reduction, the solar parallax equal to 8"'90, and 
the apparent declination of the star+ i6°45'5i"'84. It should 
be remarked that the north limb of the planet was full, and 
that the correction for defective illumination of the south limb 
was so small as to be quite insensible. 



Jan. 1^77. Mr, Plummer^ On Oar^unciion of Venus and X Oem, 103 



2 

:8 



^ ro w « ro 



^ 



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m Ov OS m O 

• ••_•• 

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I + + + + 



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M o o o ^ 

+ + + + I 




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Vh to fo fo w 

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I I i I I 



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2- = g^ S-^ 



o 

+ 



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+ + 



p 

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+ + 






III, ? I 5" ? 5 

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M 5^ c 00 o 



I04 Mr. Plnmmer, On Oor^unction of Venus and \ Oem. xxxyil 3, 



In comparing the observations with the Ephemeris we may 
obvionsly employ whatever value of the planet's semidiameter we 
please, and I have, therefore, adopted that which best satiflfies 
the observations themselves, namely 8'' '698 at mean distance. 
This is very slightly larger than that determined by myself with 
the donble-image micrometer in 1873 (8'''66i), but is less than 
the well-known determination of Mr. Maine (8''' 7 75). In spite 
of the unsatisfiEkctory state of the sky, an analysis of the indi^ 
vidual bisections shows that the probable error of a single set of 
observations does certainly not exceed o''*2 1, and it was, therefore, 
very disappointing to deduce the marked discordances that ooonr 
in the 7th column. If, however, we assume that the apparent 
semidiameter of the planet, owing to irradiation, did not remain 
constant before and after sunrise, but diminished in proportion 
as the neighbouring sky became more and more illuminated, an 
explanation of these anomalous results is possible, and their 
true significance will be apparent when exhibited in the fol- 
lowing form : — 

Mean excess of planet's^ 
observed N^.D. over 
that of Ephemeris, 
giving weights as 
above 



/Set 



Apparent excess of ob- 
served semidiameter 
over that assumed in ^ 
the previous reduc- 
tions. 



}f 



)* 



>» 



ti 



»> 



»» 



}» 



»» 



\" 



I 

2 

3 

4 

5 
6 

7 
8 

9 
10 



+0*268 

+0-583 
+ o*8o6 
+ 0*229 
+ 0-114 
—0-461 
—0-049 

-0847 
— o-2o6 

—0-128 

-1-879 



Deiore. 01 otMerratioii* ^ 



m 



4 
3 
3 

3 

2 

2 
2 

4 

3 
I 



16 27 
16 40 
16 571 



1 



17 
17 



5 
15 



17 3ix 
17 54 



18 
18 



9 

22' 



Greenwich Mean Time of Sunrise at Orwell Park 



18 40 
16 44 



Not only do these figures show a gradual decrease of the ap- 
parent semidiameter, and a more sudden diminution at the 
moment of sunrise, but dividing them into three groups and 
taking the mean of each we shall arrive at a pretty fair approxi- 
mation to the amount of variation due to the several states of 
illumination of the sky. Thus the mean of sets 1 and 2 shows 
that before sunrise the contacts were made too remotey and the 
measured semidiameter was consequently too great, by the 
quantity o"*679 C^**- 7)' ^^^ ^^^^ three sets, which were 
taken when the Sun was very low, yield an average of only o"*ol3 
(Wt. 8), as the excess of the measured semidiameter over the 
assumed value. The mean of the sots 6-9, observed after the 
Sun had fairly freed itself from the haze of the horizon, shows 



i877- ^'"'^ ^enning^ Ohservationa of Shooting Stars. 105 

ilae contacts to have been made too close by the quantity o"'273 

{jS^t, 11), the observed semidiameter being too small by that 

ttxxioant. The final resnlt shows nnmistakeably that the effect of 

ilie cloud throngh which this set was observed had been to cnt 

off the sharp cosp altogether, and to reduce the planet more or 

\e8S to the oblong figure artificially produced by Mr. Christie. 

In the paper to which I have already referred (^Monthly 

NotieeSy vol. xzxiii. p. 562), I have stated that there can be little 

donbt that the amount of irradiation of the disk of Verms varies 

from day to day with the transparency of the atmosphere. I 

We only to add, that the preceding observations prove beyond 

qneetion that such changes occur at much smaller intervals, and 

ihat Dear the hour of sunrise or sunset are of such magnitude 

as to require careful elimination in all observations of accuracy. 

FmaUy, we may conclude that for the determination of solar 

parallax by the method suggested by MM. Kriiger and Dunkin, 

each limb of the planet will require to be observed simul- 

taneoasly or nearly so, in order to evade this peculiarity ; and 

tliafc had this been provided for at both northern and southern 

stations a valuable result would most probably have been 

obtamed. 

Orwdl Park Observatory, 
1876, December 12. 



OhtervaUons of Shooting Stars, April to December , 1876. 
By W. F. Denning, Esq., F.M.S. 
{Communicated by the Sev. B. Main^ MJL, FM.8.) 

The following list of 51 radiant-points were deduced from the 
paths of 766 shooting stars observed and registered at Bristol 
during the nine months, April to December, 1876. About 1,050 
were seen altogeiher witlun this period, but some of them (in- 
cluding a number of Perseids, Oeminids, etc.) were not recorded, 
u their radiants had already been indicated with sufficient 
accuracy from other paths; and the remainder were not well 
wen, and accordingly had to be rejected. Previously to October 
iny observations were made irregularly, and not offcen continued 
&r bng periods, but during the last three months of the year 
the sky was watched on eveir fine night for several hours, 
generally before midnight. Tnis will account for my having 
Men many more meteors in the autumnal months than in the 
•pring and summer. In October, November, and December, 
during watches amounting in the aggregate to 69^ hours, 532 
loeteors were seen, and 447 of them registered. Of the total 
munber obeerved, 322 were noted in 49 hours' watching before 
nudnight, and 210 of them in 20^ hours after midnight (chiefly 
between 3 and 6 a.m.), so that the rate of frequency a.m. 
mUilj exceeded that p.m., and this was especially marked in 
Nofember. During the preceding months I did very little work 



io6 Mr, Denning^ Observations of Shooting Stars, xxxvn. 3, 

A.M., and have no data to make the same comparison. The 
chief showers of the period under review were the Perseids 
(August 10), the Geminids (December 12), the Gassiopeids 
(July- August), the Draconids (July-August), the Muscids (Octc 
ber 15), the Tauridsl. (November 8), the Taurids 11. (Decem- 
ber 6), the Aurigids (November and December 13), the Leonids 
minor (November 25-28), etc. About 40 of the positions in. 
eluded in the list are redeterminations of showers already known 
or suspected, and in regard to the latter these confirmations will 
be useful. The remainder appear to be new, and were princi- 
pally observed in the mornings of November and December, and 
one of them (a bright and somewhat active display of slow 
meteors) was seen in the evenings — ^notably on December 6, when 
it supplied nearly one-half of the visible shooting stars, as did 
the Geminids on the night of December 12. A feeble and very 
late return of the Leonids was observed on the nights of Novem- 
ber 19-20 (or A.M. 20-21), but cloudy weather had prevented a 
look-out on the few preceding nights. From the same cause the 
Lyraids (April 19-20) entirely eluded me. The Orionids (Octoi 
ber 17-19) appear this year to have been but feeb]y shown, and 
I saw few of tnem; but there was much cloudy weather at about 
that time also, wholly preventing a watch on several nights, and 
thus the maximum 01 the shower may have escaped me, as in other 
cases, for from the results of a single year's observation little 
can be expected to be done in determining durations and inten- 
sities of meteor showers, and some of &e brightest and most 
transient will pass altogether unseen. It is only by observation 
extending over many successive years that so much has already 
been learned of these features in regard to many of the leading 
showers. The dates I have given in the list are those within 
which shooting stars continued to diverge from the radiants 
mentioned, and do not pretend to show the absolute periods 
over which the showers extend, though in some cases this is 
very near the truth. The list does not include some extremely 
feeble or suspected radiants, supplying 3, 4, or 5 meteors each, 
which I have held over and will endeavour to confirm another 
year. 660 shooting stars are included in the 5 1 radiant points 
actually specified, which comprised a large proportion of small 
meteors, the relative magnitude of the aggregate number regis- 
tered during the nine months being : — 

^ Tlor'l^ ~ sistmag. ssandmag. =3rdmag. =4thmag. = 5th mag. and— totaL 
29 55 150 182 234 116 =766 

Many fine meteors (including several fireballs) were seen in 
August (chiefly Perseids), and in December (chiefly Geminids), 
but in the spring months and in October they were generally 
very small, and the great majority 3rd-4th mag. Li the list I 
have given the probaole number of shooting stars recorded as 
belonging to each radiant, as this is an important detail, not only 
as showing the intensity of the shower, but also the value of 
the position deduced. I have added a column, indicating the 



i877» ■^^« J^e^ning^ Ohaervaiiatis oj SJiooting Stctrai 107 

obflerved specialities of the meteors of each shower, though, obvi- 
oxusly, not mach can be done in this respect from a single year's 
'Work, but it may lead to something more definite and satisfac- 
tory being attempted and followed ont in the same direction in 
fatnie years. The descriptions are not by any means to be held 
as conclasive (for the materials were often scanty, and sometimes 
uncertain), bat as applying only to those members of the dif- 
ferent systems that really came nnder observation, and, except 
in regard to the more active showers, they may not have afforded 
a &ir sample of the whole. Moreover, the appearance of a 
meteor is dependent in a great measure npon the position of the 
radiant point with respect to the apex of the Earth's way. Again, 
when near the radiant the path is mnch foreshortened, and the 
apparent velocity much below the average of the same shower, and 
vice versd, A white meteor on the horizon will often look ruddy, 
etc., but, notwithstanding these difficulties, the special features 
of certain showers are strongly marked and distinct from those of 
neighbouring ones, and it is an important element to consider, 
ioasmoch as it frequently occurs that contemporary radiants lie 
near together (or in the same backward prolongation of a 
ineteor's track), and it is sometimes impossible to accord the true 
^08, unless such details are noted and taken into the acconnt. 
In some systems these specialities of appearance or motion are 
strikingly evident, and serve (almost as unerringly, as direction 
of path) to indicate the real centres of emanation. Thus, as in- 
stances of extreme velocity, there are the Polarids (September- 
October), Gemellids (October-November), Draconids, etc. ; and 
&8 samples of slow motion, the Aquilids (July-August), the 
Kscida (September-October), the Geminids (December), etc. 
In the same column I have also given in a few instances the 
clfttes of observed maximum or greatest activity. 

I have subjoined a list of the observed paths of 85 bright shoot- 
ing stars recorded during the nine months. These will be useful 
^ compare with the observations of others who may have seen 
some of them and can afford materials for the calculation of the 
lights, etc. The magnitudes given are intended to show the 
^"Mtadnum brilliancy, and the comparisons are with planets and 
stars of the ist mag. I have endeavoured to give the direction 
of the paths with as much accuracy as possible, as this is im- 

Ertant in the finding of the true radiants, a column of which I 
ve affixed, indicating them. Some details of motion and ap- 
pearance are also added, but these are somewhat incomplete, 
especially those relating to colour. Generally, however, I found 
tte slow meteors more or less ruddy, while the rapid ones 
appeared almost invariably white. Several fine meteors, ap- 
PWently from the radiant in Oemini (36), belonged to the latter 
elaas, while others (of the same system ?) were noted very slow 
*nd red. This anomaly may- perhaps be explained by the as- 
sumption of a double contemporary shower in Gemini^ as in the 
caaeof the Perseids and Cassiopeids ( Angus t), and the Leonids 
ttd Leonids minor (November). 



io8 Mr, Denmn^f OhservaHons of Shooting Start, XXXVIL 3 



I 




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Jan. 1877. ^^' J^^nning, OhservaJums of Shooting Stars, 109 




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110 Mr, Denning y OhservaUona of Shootiiig Stars, XXXYU. 3, 



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Jan. 1877. -^yfr. Denning, OhaervaHons of Shooting Stars. 



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112 Mr. Denning^ Observations of ShooUng Stars. XXTYIL 3, 



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iB.iS77y Mr, Denning y Observaiions of Shooting Siari. 113 



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1 14 Mr. Benningy Observations of Shooting Stars, xzxyil 3, 



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]an. 1877. Mr. Venning, Observations of Shooting Stars, 115 




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1 16 Ohs, of Occultations of Stars by the Moon^ etc. 



Ohservations of OccviUations of Stars by the Moon, a/nd ofThenon 
of Jupiter's SaieUiies^ made at the Boyal Observatory ^ Qreewik 
in the year 1876. 

{Qmimunicated by the Axtronomer Boyal.) 
OccuUatUni of Stars by the Moon, 



Day of 
Obi. 



Fhenomenon. 



X876. 
Feb. 2 Disapp. of 27 Arietis 



Tdesoope.* Power. 
KEq. 140 



April 7 



If 



»* 



ft 



1 1 Beapp. 

May 5 Disapp. 
Aug. 13 „ 
Nov. 29 



ft 



f» 



If 



Piam XIL iii 
/Viiginifl 
(Soorpii 
50 Virglnis 
X'Tauri 
47 ArietiB 
47 Arietis 



If 



Altaz. 



tt 



E. Eq. 
Altaz. 
E. Eq. 
S.E. Eq. 



*t 
100 

)f 
140 

100 
140 
220 



lCoon*8 
Liiiib. 

Dark 



Mean Solar 

Timeot 01 
Obeervmtion. 
h m ■ 

6 30 19-3 



8 27 53-9 
II 38 217 

11 56 si'^ 

12 o 43*0 
Bright 12 19 20*5 
Dark 7 57 284 

7 57 ^'2 



t* 



f) 



t$ 



f» 



tt 



Phenomena of Jupiter* s Satellites, 



tt 



^^^^ SateUite. 

1875. 
Apr. 8 1(a) 

„ I 

„ I 

15 I 

20 n{b) 
u 

1(c) 

1(d) 

I 

n 

II 

6 U{e) 
9 I(/) 

20 n 
n 



If 



tt 



May I 



It 



)) 



If 



tt 



tt 



n 



Phenomenon. 

Ooe. reapp. first cont 
bisection 
last cont 
Ed. disapp. 
Tr. eg. first cont. 
„ last cent. 
Ed. disapp. 
Occ reap, first cont. 
„ last cont. 
Tr. ing. bisection 
„ last cont. 
Occ. reapp. first cont. 
Tr. eg. last cont 
Occ. disapp. first cont. 
bisection 
last cont. 



Mean Solar Mean Solar 

Tdeaoope. Power. Time of Time from 

Obaervatian. NA. 

h m s h m ■ 



S.E. Eq. 130 



It 



ff 



tt 



»» 



E. Eq. 



it 

>» 
tt 

tt 
tt 
t* 
)) 
it 
»» 
t> 
t» 



If 

ff 
140 

)f 
ft 
it 
tt 
it 



it 

it 
310 
140 
310 

ft 
tt 



3 18 28 

3 20 52 I" 13 18 

3 26 59 

2 II 56*3 12 12 1*5 

I 28 58 

1 31 " 
o 28 11*4 10 28 2*3 

2 59 37 



I 



II 26 



3 I 41 
3 29 36 

3 31 51 

o 19 

1 53 10 

1 59 21 

2 I 50 
2 3 20 



1- 

1- 



28 



10 3 

11 51 

12 I 



* The clear aperture of the object-glass of the S.E. Equatoreal is 12} ind 
the East Equatoreal 6*7 inches, of the North Equatoreal 4*1 inches, and < 
Altazimuth 3{ inches. 



TelMoope. 


Power. 


Mean Solar 

Time of 
Observation, 
h m 8 


Mean Solar 
Time from 

N.A. 
h m ■ 


Obaerrer. 


If 


)f 


" 45 53 






ft 


tt 


II 47 22 


.11 49 


C 


tt 


tt 


II 49 7 


• 




» 


140 


II 29 46 


II 14 


L 


tt 


tt 


11 9 12 


II 10 


T 



Jan. 1877. Stars to be compared in B.A, with Mara, 1877. 117 

^" Sitellite. Phenomenon. 

tsjtij n Tr. Qg. first cont. 

„ n „ bisection 

„ n ,, lastoont. 

J1M24 I (g) Tr. eg. last cont 

Idj 3 in „ last cont. 

Notes. 

(«) The limb of JvpUer was yery tremnlons. 

Wi (<0> (^) ^^® limbs of the planet were badly defined. 

(e) The first diminution of brightness was observed 2" 15* before the time here 

recorded. 
(/) The observation was not satisfiictory. 
\$) The image of Jupiter was yery bad. The recorded time is evidently 

erroneous. 

The initials L, C, AD, M, T, G, P, and HP, are those of Mr. Lynn, Mr. 
Criiwiek, Mr. Downing, Mr. Maunder, Mr. Thackeray, Mr. Graham, Mr. Pulley, 
ttd Mr. Pett respeddyely. 

Sojfol Oburvatory, Oreenwich, 
1877, Jamuuy 13. 



fi^f to he compared inB, A. with Mwrs 1877, f^ BeterminaHon of 

the Parallax of Mars. 

(Conmmnieated by the Astronomer Boyal.) 

The stars in the accompanying list have been selected from 
ibose ffiyen on the chart in the Monthly Notices for 1875, 
Noyember, as being snitable for eqnatoreal observations of the 
differences of their B. A. and that of Mars, east and west of the 
Meridian. They have been arranged in pairs, one star preceding 
^d the other following Mars ; and as a fresh setting of the Eqna- 
toreal in N.P.D. will usnally be reqnired for each object, an 
^rval of at least three minntes of time is allowed between the 
^^^mi oi Mars and that of either star. In some cases, however, 
^ pair of stars can be found passing thronsh the same field as 
Uan^ and here a much smaller interval wul be sufficient, with 
tbe advantage that a larger number of comparisons can be made, 
^ sets being repeated in more rapid succession. Such pairs 
^ Btars are denoted by an asterisk. In order to eliminate as far 
^ possible the effect of error of adjustment of the Eqnatoreal, 
Btars have been selected at about equal distances north and south 
of lfar«, and in some few instances where this was not praoticablei 



xi8 Stars to he compared in B,A, with Mars 1877, xxxrii. 3, 

two stars on one side have been given with a view to seonring a 
doe balance, it being intended that these two stars should be 
observed altematelj in combination with Mars and the other star. 
Preference has been ffiven to the brighter stars, but there is suoh 
a paucity of stars in tiua region that it has sometinies been neces- 
sary to go as low as the ninth magnitude. 

The plan of observation requires a firmly-mounted Equa- 
toreal, which can be securely clamped in Bight Ascension, 
and provided with a transit eyepiece having a system of pa- 
rallel meridional wires at convenient intervals. A number 
of sets of transits of Mars and a pair of stars should be taken 
in as rapid succession as possible in the evening, when Mars 
is east of the meridian and as far from it as practicable;^ 
and a corresponding number of Mars and the same pair of 
stars in the early morning, when Mars is far to the wast, the 
Equatoreal being firmly clamped for each set. Both limbs of Mars 
are in all cases to be observed, over alternate wires, or otherwise, 
as may be found convenient, care being taken that the limb 
(whether first or second) observed over any particular wires in 
one set be observed over the other wires in the next set. The 
same pair of stars must be observed in the morning and evening 
(as has been mentioned), and when a change occurs from one day 
to the next, both the old and the new pair should be observed 
alternately on one morning or evening at least. If different 
observers take part in the work, care should be taken that each 
observer is charged as often with morning as with evening obser- 
vations. 

The value of the observations made at any particular station 
will depend largely on the interval between the evening and 
morning sets of comparisons ; and the choice of stations is deter- 
mined mainly by consideration of the available time-interval 
during which Mars is &x enough above the horizon and the Sun 
far enough below to allow of satisfactory observations being 
made. Taking these " horizon allowances " as i^ 26™ for lat. 
50° N., 1^ c^ for lat. 15° N., and i^ io°» for lat. 35° S., the 
*^ available time-interval " has been computed for Uiese three 
latitudes ; and the following table has been formed, showing, at 

intervals of seven days, the square of the quantity -^, ^ 

dist. of Mars 

X COS. of station's latitude x available time-interval, which 

may be considered as a roughly approximate value of the square 

of the parallax factor, and which gives the combining weight of 

these observations in the determination of the Sun's Equatoreal 

Horiasontal Parallax. 



Jan. 1877. far Determination of PartiUax of Mars. 119 

(Parallax Factory 







Latitude 50'' N. 


15ON. 


35^8. 


July 


22 


23 


155 


180 




29 


34 


202 


216 


Augost 


' 5 


50 


259 


269 




12 


72 


329 


325 




19 


97 


405 


383 




26 


126 


487 


444 


Sept. 


2 


156 


563 


492 




9 


152 


586 


480 




16 


141 


496 


413 




23 


125 


410 


330 




30 


104 


330 


256 


Oct. 


7 


86 


263 


194 




14 


71 


208 


144 




21 


57 


163 


106 




28 


50 


129 


78 



Paivrs of Stars to be comjpared m B.A, with Ma/rs. 

(TIu Kos. are those of Weisse's Beesel, Cat, 8UU. in Zonis Begiomontanis. 
The mean places of the Stars for 1877 are given in the Monthly Notices, 
£>r 1875, Noyember.) 

Ofj, 

^^J n 322, 565 427*. 508* 



26 



»» fi 



^ 427. 586 

28 






39 

30 427, 619, 629 



31 
iig. I 

2 

3 

4 

5 
6 

7 
8 

9 
10 



** 

» 

it 
n 
n 
n 

M 

99 



120 Sta/rs to he compared in B.A, with Ma/ra^ 1877. xxx^ 



1877. 

Aug. II 




A^7» 619 






12 




f» 






13 




fi 






14 




II 






15 




427i 583 






16 




>f 






17 




tt 






18 




377i 583 






19 




» 






20 




tt 






21 




377. 497 






22 




If 






23 




315. 497 






M 




315, P. XXII 1. 


109 




25 




If 






26 




265. 497 






27 




265, 402 




309* « (R.A. 19* 55- 

N.PJ). IOI«2^ 


28 




9$ 




286*, 385* 


29 


^ Aquarii, 402, 403 






. 30 




tt 






31 


^ Aqnarii, 373 




185*. 309* 


S^t. I 


Lai. 


45504. 309 




It 


2 




.. 




.1 


3 




57. 265 


Lai 


.45504*. 309* 


4 




If 




t. 


5 




1* 




.1 


6 




49, 228, 270 




57*, LaL 45504* 


7 




1276, 185 




.1 


8 




It 




1. 


9 




1 261, IaI 45504 




1261*, 57* 


10 




tt 




.. 


II 




1204, 57 




II 


12 




*• 




1. 


13 




>f 




II 


14 




1129, 12, 14 




1204* 1 261* 


15 




1* 




.1 


16 




If 






17 




1079, 1261 




II 29*, 1204 


18 




11 







JaB.i877. Mr.Ahhe,OnMiichd'9Oh80rv<Uion8atOtnc%nn(Ui. 121 



OMl 



X877. 






8^19 


966, 1204 




ao 




966*, I129* 


31 




ff 


23 


74Aqiiarii, 1165 


ff 


?3 


If 


If 


24 


n 


f» 


25 


If 


ff 


26 


f» 


If 


«7 918, 


"29 935. 1156 


7oAqiiarii, 1079 966*, lis 


28 


yoAqnarii, 1079 




29 


ff 




JO 


fi 




. I 


If 




2 


n 




3 


n 


74 Aqnarii (coigimetion) 


4 


II 


ff 


5 


l» 


ff 


6 


If 




7 


II 




8 


ff 




9 


If 




10 


7oAquArii, 1047, 1079 




II 


II 


926*, 1007* 


12 


II 


II 


13 


ff 




14 


70 Aquarii, 1065 




15 


910, 1047 


70 Aqnarii, 1122 


16 


7oAqiiArii, 11 22 


946*, 7oAquarii*, 1020* 


17 


7oAquarii, 11 20 


977*1 946*1 1020* 1017* 


iS 


II 


994*1 933*1 1017* 



Rof/al Ohservatory, Greenxmch^ 
1877, January 13. 



On 0. M, MitcheVs Observations at [Cincinnati, 
By Cleveland Abbe, Esq. 

In a note to his recently- published "Reference Catalogue** 
Mr. Knobel calls attention to the fact that copies of MitcheVs 
Sidereal Messenger are very rare in England, and to the Supple- 
mentary note in Nature (November 9, page 49). I would add, 



122 Mr. Ahhcy On MUcheVs Ohs. of Double Stars zxxyn. 3, 

that complete sets of this interesting periodical are almoet 
eqnallj as rare in America.* Barer still is to be found nowa- 
days the excellent text-book for schools and hand-book for ama- 
teurs, published in 1849, in Cincinnati, New York, as '' Mitchel's 
edition of Burritt's Geography of the Heavens" In this book 
Mitchel published numerous notes based on the work done 
during 1845-48 at his Observatory, and I have thought it may 
interest members of the Astronomical Society if I copy trom, it 
for their use the record of double star positions observed at Cin- 
cinnati. These few figures, however, convey but a faint idea of 
Mitchel's activity during those years : in my annual reports, 1868, 
1869, and 1870, 1 have given a nearly full list of his publications, 
and expressed the hope that I should be able to prepare for publi- 
cation such of his observations (especially the very extensive 
series of zones of faint stars) as gave promise of being useful ; 
and although this is now become a very difficult matter, owing to 
the death of Mitchel and his faithfal assistant Twitchel, yet 
possibly my successor may be induced to undertake it. 

In the accompanying table reference is given in the last column 
to the page of Mitchel's edition of Burritt. I have also included 
the name of NebulsB, etc., concerning which Mitchel gives some 
notes as to their appearance at Cincinnati ; these notes are 
generally somewhat general and unsatisfactory in their nature, 
but I shall be happy to communicate them in full if desired. I 
fear lest an occasional typographical mistake may have crept 
into the measurements here given ; but possibly these may at 
some future time be rectified if ever the original observer's 
note-book can be found.f 

W(uhing[tonf 
1876, December 15. 



Ohservations of Double Stars, by 0. M. Mitchel, made between May 1841 
and May 1848, with the 12-inch Bsfractor, at Cincinnati. 

{From MUcheVs " Geography of the Heavens,"* New York, 1849.) 

«j^ Constellation 

^^' and Object. 

1 38 Piscium 

2 55 » 

3 T Cassiopciae 

4 ^ t. 

5 65 Piflcium 

* The Astor Library, in New York City, possesses a few of the last pub- 
lished numbers, which are, I believe, wanting in all the other sets that I have 
hitherto seen. 

t The names of Nebulae are omitted from the Table as printed, and the 
Double Stars have been rearranged in order of Right Ascension. — Ed. 



BJL 

h m 


Dec. 


Position- 
Angle. 


Distance. 


Epoch. 


RV 


9 


/ 

+ 7 59 


/ 

235 59 


// 
4*646 


184765 


S 


31 


+ 20 33 


191 52 


7014 


184765 


S 


39 


+ 50 34 


146 25 


2 24 


184760 


4 


39 


+ 56 57 


loi 20 


8-59 


1847-60 




41 


+ 26 50 


297 32 


• • • 


184765 





Jan. 1877. 



madoj 1 845-1 848, cU Cincmnati. 



123 






GcMMteU»tioii 
'^ and Object. 




Dec. 


Position- 
Angle. 


Distance. 


Bpoch. Page. 


6 36 Andromedse 





46 


/ 
-I- 22 


330 14 


M 
1050 


1847*70 


39 


7 ♦OM8ioptiiB(A&B) 


I 


14 


+ 67 14 


102 37 


30*394 


184760 


49 


S „ „ (B&C) 


»l 


II 


i» II 


253 7 


32-856 


1847*60 


50 


9 7Arieti8 


I 


44 


+ 18 30 


175 37 


9184 


184765 


60 


10 sPiflciuin 


I 


53 


+ I 59 


330 3 


... 


184765 


55 


II 7AiidiQmed« 


I 


54 


+41 


no 


0*40 


184660 


40 


U YVixginis 


12 


33 


- 34 


357 28 


309 


184760 ] 


[16 


13 Corns Ber. (A & B) 


12 


45 


+ 22 7 


40 4 


r3»6 


1847*57 ] 


135 


H „ (A&C) 


it 


II 


II II 


125 31 


*• . 


1847-57 1 


»35 


1$ S4Viigini8 


1335 


+ 4 21 


231 5 


348 


184706 ] 


[18 


16 vBootis 


14 33 


+ 17 6 


96 57 


828 


184760 ] 


[28 


17 C » 


H 33 


+ 14 25 


128 24 


6924 


184762 ] 


[28 


tf« ,. 


14 


38 


+ 27 45 


320 50 


2-568 


1846*66 ] 


[28 


'9 i .. 


1444 


+ 19 46 


317 44 


6-482 


184763 ] 


[29 


» 39 ., 


14 44 


+49 22 


37 


400 


184760 ] 


[29 


« 44 .. 


14 


S8 


+ 48 16 


238 20 


3738 


1847-62 ] 


[29 


22 /iSoorpii 


15 56 


— 19 21 


26 22 


1368 


1846*50 J 


147 


23 5ULibm(A&B) 


15 58 


-10 55 


24 52 


097 


184648 ] 


143 


H « ,. (A&C) 


t> 


f» 


II II 


7442 


716 


1846*48 ] 


143 


3$ r Seorpii (A & B) 


16 


2 


-19 2 


37 57 


1*2 


i846*(?) : 


[46 


as „ „ (JAB&C) 


i> 


II 


II II 


338 29 


40*0 


i846(?) 1 


[46 


37 vSeorpii 


16 


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271 5 


22*34 


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^7 


28 „ 


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19 


— 26 4 


90 


25 


i845-5(?) ] 


[46 


29 XIVPiazzi88 


16 


20 


- 7 45 


304 14 


5*292 


184770 1 


[86 


30 X Ophiuchi 


16 


22 


+ 2 20 


3 42 


1*42 


184765 ] 


183 


31 (HeicuHs 


16 


35 


+ 31 53 


109 12 


1078 


1847*70 ] 


'63 


32 11 „ 


16 


37 


+ 39 13 


] 


inseparable 


] 


163 


33 


16 


54 


+ 8 41 


146 57 


0*826 


184770 ] 


185 


34 MDneonis 


17 


2 


+ 5441 


190 57 


2*90 


1847*70 ] 


133 


35 36 


17 


5 


— 26 21 


215 49 


4-27 


184762 1 


[85 


36 •Hercnlis 


17 


7 


+ 14 34 


117 36 


492 


1847-62 ] 


[62 


37 


17 


17 


+ J5 45 


62 33 


3654 


184760 ] 


(85 


3^ DncoDis 


17 25 


+ 50 59 


266 20 


3*03 


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133 


39 r Ophiuchi 


17 54 


- 8 10 


229 24 


0779 


1846-51 1 


^83 


40 P« 70 Ophiuchi 


17 57 


+ 2 32 


12045 


553 


184755 1 


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18 


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253 


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42 •Ljifc(A&B) 


18 


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39 30 


20 25 


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124 Mr. LasseUj On Space-penetrating Power. xxxvn. 3, 



No. 


Oonstellatlon 
and Object. 


B.A. 
h m 


Deo. 
/ 


Positioii- 

Angle. 

/ 


Distance. 

u 


Bpooh. 


• 


44 


Aqniln (B & G) 


18 54 


- 55 


76 


1576 ] 


[847*60 


i7< 


45 


Aqniln 


18 57 


+ 6 18 


152 28 


9492 : 


[847-65 


I7< 


46 


23 Aqniln 


19 10 


+ 48 


12 9 


3*57 ^ 


[84767 


IT 


47 


AquiUe (A & B) 


19 28 


— 10 46 


319 4 


2'54 1 


[847-60 


n 


48 


» (A & C) 


It it 


II II 


169 17 


... 


••• 


If 


49 


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19 37 


+ 10 23 


276 36 


4*33 J 


[84772 


17 


50 


IT Aqnile 


19 41 


+ 11 25 


123 9 


I -20 ] 


[84766 


17 


51 


a* Capricorni 


20 9 


-13 2 


144 II 


636 ] 


[846-67 


19 


52 


P 


20 19 


-18 20 


176 56 


3094 J 


1847-70 


19 


53 


XXPiazri, 376Equulei 20 47 


+ 3 55 


28745 


1-874 1 


[84765 


iS 


54 


« Equnlei (A & B) 


20 51 


+ 3 41 


288 6 


0574 ] 


[84760 


18 


55 


» » (A & 0) 


t« If 


II II 


76 25 


1 108 ] 


1847-60 


iS 


56 


X „ 


20 54 


+ 6 33 


227 42 


19 1 


[847-60 


iS 


57 


12 Aquarii 


20 55 


— 6 27 


191 30 


823 1 


[84763 


19 


58 


61 Cygni 


20 59 


+ 37 58 


lOI 2 


173 1 


[847-50 


16 


59 


29 Aquarii 


21 53 


-17 43 


242 8 


4*466 1 


[847*70 


IS 


60 


41 » 


22 5 


—21 51 


120 22 


4326 1 


[84770 


15 


61 


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22 6 


4- 16 24 


331 29 


803 1 


[847-65 


I< 


62 


CAqoarii 


22 20 


— 50 


346 42 


3-948 ] 


1847-70 


11 


63 


37 Pegasi 


22 21 


+ 3 37 


121 46 


098 ] 


[847-70 


I^ 


64 


Aqnarii 


22 34 


- 9 8 


3H 35 


1-82 ] 


1847-70 


I« 


65 


Piscium 


23 37 


- 37 

• 


227 33 


2702 


1847-65 


• 



On the Space^jpenetrating Power of Mr, LasselVs 2-foot and /^-foot 

Eeflectora. By W. Lassell, Esq. 

In the Monthly Notices for December is a note hj M. Otto 
Strave, in which, quoting from a previously written paper, he 
says, '' The space-penetrating power of Mr. Lasseirs new 
(4-feet) instrument can hardly be estimated superior to that of 
ours (the Pulkova 15-inch) Refractor. " There appears to me to 
be something so erroneous in this conclusion, that although veij 
averse to controversy, and especially to enter the lists with my 
very distinguished firiend, M. Struve, I crave permission to state 
my greatly differing opinion, and the grounds on which I have 
formed it. ^ 

To begin with a comparison of the powers of my 2-foot 
Equatoreal with those of the Pulkova telescope. About the year 
1847 and later, I was engaged, as opportunities offered, in a 
diligent scrutiny with the view of verifying the fainter Satellites 



Jan. 1877* ofhU 2'foot and i^-foot Beflectors, 125 

of Uranus, presumed to have been discovered hj the late Sir 
William Herschel. It would appear from Professor Stmve's 
commnnication to the Monthly Notices ^ vol. viii., pages 44 and 
139, that he was then engaged in the same carefal search; and 
he annonnces, with some confidence, his verification or re-dift- 
oovery of at least one of Herschers satellites, namely, that whose 
period was announced by Herschel to be 5^* 21** 25™, adding that 
he had no doubt of the identity of the two objects, and that his 
observations " completely prove the existence of HerscheVs first 
supplementary satellite.'* Yet the detailed observations at page 
46 do not seem to me sufficiently exact or consistent to justify 
this conviction ; and certainly the long series of supplementary 
observations of the Satellites of Uranus has made the conclusion 
irresistible that this rediscovery must be given up, and that the 
Polkova telescope was not equal to the task then set before it. 

The interior faint satellites, now recognised as Umhriel and 
Arid, were first certainly seen by me in 1847, but I was not able 
to give what I thought a sufficiently distinct account of them 
until 1851 ; and I would especially direct attention to my letters 
of the 13th and 29th November in the latter year {Monthly 
Notices, vol. xii., page 15), as proving by the precision, certainty, 
and frequency with which the objects were seen, that the 2-foot 
Reflector must have been even greatly superior to the 15 -inch 
Refractor. I may, perhaps, add also the opinion of the late 
Mr. G. P. Bond, expressed verbally to myself, that my 2-foot 
telescope was sensibly more efficient than the Harvard Telescope, 
which may be called a facsimile of that at Pulkova. 

I will now refer to vol. xxxvi. of the Memoirs, containing 
the record of my observations at Malta with the 4-foot Equa- 
toreal, as proving the superiority of that telescope in illumina-' 
ting or ** space-penetrating ** power, to the 2-foot Equatoreal. 

At page 34 an observation of Uranus and his Satellites is 
recorded, together with an expression of my opinion of the com- 
parative efficiency of these telescopes on these objects, and 
asserting the great superiority of the 4-foot. Again, at page 36, 
on September 27th there is recorded an observation of ^ Cygni, 
in which the 2-foot is again mentioned, with a remark in 
faivour of the 4-foot. Further, at pages 7 and 8, observations 
of the Satellite of Neptune made on August 2nd, September 
22nd, and October 19th, are given, when the satellite was ob- 
served nearer to the limb of the planet than it had ever been 
seen in the 2-foot. Moreover, I may remark that the observation 
of a faint satellite very near to its primary in two telescopes 
dififering gpreatly in size, tells disproportionately ap^inst the 
larger one ; since the greater brightness of the planet diminishes 
the sensibility of the eye for detection of the satellites — in addi- 
tion also to the greater disturbance of the atmosphere with the 
larger aperture. 

Lastly, in further corroboration of the superiority of the 
4-foot, I may suggest a comparison of the figured Nebulee in this 
Tolume with such of them as are contained in vol. xxiii. 

K 



126 Mr, Brettf On (he Specular BefUxion Hypothesis, xxxvn. 3, 

of the MemoirSy in mj paper giving observationB with the 
2-foot. 

I conclude with remarking that Professor Struve's anfavoiir. 
able impression may perhaps in some degree have arisen from 
his visit to Malta having been made at a time of the year when 
the atmosphere is occasionally much disturbed by storms, which 
are of course greatly to the disadvantage of a very large tele- 
scope. 

Bay Lodffe, Maidenhead, 
1877, January 23. 



The Specular Bejlexion Hypothesis, and its bearing on the Transit of 

Venus, By John Brett. 

There was a phenomenon observed at the transit of V&nus 
(the ring of light at the planet's limb), which, as far as I know, 
has not hitherto been explained, and my present purpose is to 
show that the specular reflexion hypothesis has an important 
bearing on this subject. If, in addition to a burnished r^ectinff 
surface, we suppose Venus to have a translucent envelope ot 
great density, it appears to me that all the elements necessaiy for 
a complete explanation of the mystery are at hand ; at all event(^ 
it is possible on these terms to produce a very similar phenomenon 
experimentally. 

In my last I ventured to suggest a reason for believing tha 
surface of the planet to be in a molten or vitrified state. 

That suggestion was peculiarly fortunate in having attracted 
the attention of Mr. Christie, whose investigations afford, at all 
events, invaluable data for studying the subject, if not (as T 
believe) a complete confirmation of the hypothesis. Vide last 
Number of the Monthly Notices, 

The theory of specular reflexion is, of course, perfectly well 
understood, and its phenomena in the case of Venus and the 
Sun would occur as follow : — At superior conjunction we shonld 
see merely a small circular image of the Sun. In the course of 
the planet's progress in its orbit, this image would move in 
longitude and extend itself in latitude, assuming a cusped crescent 
form. Near the time of inferior conjunction it would approach 
the limb, and present an extremely attenuated rim of Ught. At 
transit this rim would completely encircle the disk, and theoreti- 
cally would never entirely disappear. Even practically, the Sun's 
light near his limb is so much weaker than at the centre, that it 
is quite conceivable that the rin^, or reflected image, might be 
observed during the earliest and latest stages of the transit. 
The position this ring would occupy within the planet's limb 
can of course be determined with accuracy by a calculation based 
on the relative diameters of the Sun and planet. 

So far the theory is simple, and has been so well understood 
for ages that no illustration is needed. 

It will, however, be perceived that any expansion in latitude 
of this extremely attenuated ring which might have been ob> 



Jan. 1877. and (he TratuU of Venus, 127 

senred at transit (and I understand that the photographs prove 
such to have been the case), wonld introduce other and more 
complicated considerations into the problem, indicating, as I 
mppose it would, the existence of a re&active envelope or atmo- 
sphere. Now, any diffusion or extension of the area of the ring 
would of course weaken the intensitj of its light, not to mention 
ihe question of absorption. Before contact, however, these con- 
siderations would not at all damage the theory. The great 
difficulty arises when we find a diffused ring of light suri'ounding 
the planet whilst actually on the Sun's disk surpassing in brilli- 
vuj his direct rays. If there are no theoretical objections to the 
planet's surface existing in a state of ^ion, or at all events, to 
bave Bo existed, it is not unreasonable to suppose that the metallic 
ooQstitnents of its substance would settle at a lower level than 
its lighter or vitreous elements : we might thus imag^e a molten 
metcJlic lustrous surface overlaid and protected by an envelope 
of glass. 

There is, I suppose, no doubt that the lenticular action of an 
itoiOBphere of great refractive power would be effective to bend 
o?er the limb, and produce in a condensed state, some of the rays 
which impinge on the planet immediately beyond the limb, and 
in that way it seems to me that a certain degree of increased 
brilliancy would be produced ; but if we are allowed to assume 
the existence of a vitreous envelope, it is evident that, in addition 
to the correction of the divergence of such rays as have been 
reflected from a zone of the burnished surface unmediately be- 
hind the limb, a quantity of light reflected fi*om another zone 
still farther beyond the limb, would be condensed by interior re- 
flexion from the surface of the vitreous envelope, acting in the 
KDse of a concave mirror, and produced over the limb towards 
the Earth, so as to give a luminous halo of greater brilliancy 
than the Sun itself. The little instrument which I invite the 
I'ellows to look into after the meeting shows that such a result 
<*n be experimentally produced. 

It consists, first, of a small globe representing Venus suspended 
within a tube; secondly, of a collimator; and, thirdly, of a 
niicroscope focnssed upon the limb of the little globe. The little 
globe or model of Venus consists of a glass bulb filled with 
Dierenry. 

When this instrument is directed to a gas-lamp the ring of 
^ndensed light is very plainly seen ; and I think that although 
the apparatus is very rudely and imperfectly made, it does all 
that can be expected of it. 

I now ask leave to add one more suggestion, as follows : — 

At the next transit it would be worth while for some one with 
^ good telescope and a Dawes-diaphragm to look at the centre of 
^enut's disk for the reflected image of the Earth. If the envelope 
^ the planet has great refractive power, I think it not impro- 
bable that it might be seen as a minute nebulous speck of light. 

38 HarUy Street, London, 
1877, January 12. 



ia8 Mr, Erck, Improved Mode of viewing the Sun, . xxxyii. 3, 

An Improved Mode of viewing the Sun. 
By Wentworth Erck, Esq. 

A Barlow-lens is first employed to enlarge the image, and 
then, by means of a small, nnsilvered, elliptical, plane, glass 
snrface a minnte portion of the pencil, forming the enlarged 
image, is deflected into the eyepiece; the remainder of the 
pencil, which may be -iV^fths of the whole, escaping, freely, and 
therefore withont heating, into the open air. 

For example : The image formed by my object-glass is an inch 
in diameter; this is doabled by a Barlow of 8-inches nega- 
tive focas, while the minor axis of the elliptical reflector is only 
^rd of an inch. 

. Thus it is evident that only ^th of the entire image is trans- 
mitted to the eyepiece, and the remaining ff ths escape freely 
into the open air. 

But of the ^th that woald reach the eyepiece, only iV^ ^ 
actually reflected by the nnsilvered snrface, so that the amonnt 
of heat reaching the eye, under these arrangements, is but ^ii^^ 
of that which would reach the eye directly viewing the original 
image of the Sun. 

As it is desirable to be able to examine the edge of the 
disk in the centre of the field, and also desirable that no 
part of the pencil should impinge upon metal work, it follows 
that the clear aperture of the Barlow should be at least twice 
the diameter of the principal image ; and the tube, carrying the 
eyepiece, should be four times that diameter. 

The most convenient form of reflector is a cylinder cut at- an 
angle of 45^, and having its surface and base polished to prevent 
•soape of heat except at the base. This cylinder is supported on 
a very light arm, exactly as in a Newtonian. 

1 can spt'ak from experience of the grreat advantage of this 
arrangt>mont« the eyepiece remaining even in summer perfectly 
oooU with 7 finches aperture, and the definition unimpaired so 
long as the telescope is kept accurately following the Sun to 
pn>vont his rays striking on the tube. 

The subjoined sketch is ^th true size. 



r 






MONTHLY NOTICES 



OF THE 



ROYAL ASTRONOMICAL SOCIETY. 



Vol XXXVII. February 9, 1877. 



No. 4. 



William Huooins, Esq., F.It.S., President, in the Chair. 

Geo. Francis Hardy, Esq., Bothbnry House, Strond Green, 
Fbabnry Park, N. ; 

John Sidney White, Esq., 13 Bolton (hardens. South Ken- 
tington, S.W. ; and 

A. Mason Worthington, Esq., B.A., Sandiway House, 
Alfcrincham; 

were balloted for and duly elected Fellows of the Society. 



Bbfobt of the Council to the Fiftt-seyenth Annual General 

Meeting of the Society. 



Progress and present state of the Society : — 





1 

204 

+ 9 

-2 

+ 1 

• • • 

• • • 

212 


lumbers!, 1875 


Since elected ... 

l>«e«8ed 

^^aovaU 

\ R«ngned 

■ExpeUed 


1 December 31, 1876 



I 



s 



348 



+ 20 

- 7 

— I 

- 6 

— I 

353 ' 5 



i 



a 

i 



I' 



s 



1 



I 



- I 



I 



1 



566 



\S7S 



I 



42 



42 



608 



620 



130 Report of the Council to the XXXTO. 4, 

REPORT OF 

The Report of the Auditors not having been received at tlie 
following copy of the Treasarer's signed Report submitted to 

Mr, WkUbread^s Account as Treaawrer of the Boyal 
RECEIPTS, 



Balance at Bankers*, Dec. 31, 1875 

In hand of Secretair of Librazy dommittee : 

On account of Library Eiqpenses 

„ Tumor Fnnd 

In hand on Petty Cash Account 

Dividend on 1^3,700 Consols 

„ £5,200 New 3 per Cents 

„ £4,000 Consols 

M £5,200 New 3 per Cents 

Beceived on account of subscriptions : 

Arrears of contributions ... ... ... 

237 Contributions for 1876 

On account of ditto 

28 Admission Fees ... 

20 first Contributions 

II Composition Fees 

Sale of publications at Society's Booms 

M „ Williams & Norgate*s ... 

Balance of Horroz Memorial Fund 

Bequest of the late T. C. Janson, Esq., to t^e 

iUOO J7 il Il Cl ... ... ■*• ... ... 

Bequest of the late R. C. Carrington, Esq., £2,000 
Consols, transferred to the Society's account, at 94 

Due to Assistant Secretary, on Petty Cash 
Account, Dec. 31, 1876 



£ 9. 


d. 


548 18 


9 


32 3 





21 





13 4 


II 



£ 9. i. 



55 





9 


77 


7 





59 


5 





77 





6 



615 6 8 



s68 13 3 



106 I 






497 14 

200 

60 18 






33 II 

• • • •• • 

52 18 8 
23 I 

• • • •• • 


699 4 
231 

75 19 
38 IS 





8 



• • • ••• 


200 





• • • •• • 


1,880 





• • • • • • 


2 18 


8 




£4,011 17 3 



Sam. Chas. Whitbbbad, 

IV'easuret, 



Peb. 1877. Fifty-aeventh Annual Oeneral Meeting, 



131 



THE TREASURER. 

tiiDe of the revision of the Annnal Report of the Ooanoil, the 
tbe Auditors is herewith appended. 

Mrmomicdl Society^from Dec. 31, 1875, ^ ^^- 3^> 1876. 

EXPENDITURE. 



flUftries:— 

Editor of Monihiy Notices, 5 qoaiters 
Asdstant Secretuy, 5 quarteis 

Ineome Tax and Honae Duty 

Fbelnforance 

Pnnting: 

Spottiswoode & Co 

fi»wll, Watson, ft Viney 

Holdgate Brothers, Printing Plates... 

^^^hpgraphy, Engraving, &c. :— 

(^tham School of Photography . . . 
^- H. Wesley 

Bbding and Stitching : J. Rumfitt 
'l^—'y expenses, binding books, &c. ... 
Tnmor Fund : books purchased during year 

IGseeUaneous :— 

RooBe expenses 

Waima 

^^S^JO... ••• ••• ••• ... 

8tamps and postage 

^^BfHage of books and parcels 
Stationery and ofSoe expenses 

Expenses of meetings 

^^<^^^ and gas 

Mrs. Jackson-Gwilt's Annuity 

KttangB in Library &c. : Whitechurch Bros. 

Sun^^es 

R^^^en^ commission &c 

Ne^ <dieque-book 

InT6stmexit8 : 

PuY^cluue of £300 Consols, at 96|, including 
^^^^'HunissioD... ... 

^'^Tf^hase of £200 Consols, at 95|, including 
QonunisBion... ... ... ... 

CarxingtoQ Legacy of £2,ocx> Consols, transferred 
^ Society 8 account, at 94 .. 

BalaBce at Bankers', Dec. 31, 1876 

In hand of Secretary of Library Committee 

""^n account of Library Expenses 

On account of Turner Fund 



£ 

75 
187 



8. d. 

o o 

10 o 



364 

187 

18 



8 o 
12 o 

5 o 



5 
51 



10 o 
2 o 



28 
23 

49 
8 
8 

17 

74 
8 

5 
20 

o 

o 



7 7 
17 o 

10 8 

8 2 



6 

15 
19 
19 



o 
6 

9 
o 

6 



19 8 
o 6 
8 4 



289 
191 



10 o 



10 o 



238 I 10 



13 
22 



8 6 
3 9 



£ «. d. 



262 10 o 

5 5 o 
7 16 6 



570 5 o 



56 12 o 

39 17 3 

138 H 6 

48 16 3 



247 6 8 



481 o o 
1,880 o o 



273 '4 I 
£4,011 17 3 



Sam. Chas. Whitbrbad, 

TVeamrer. 



L 2 



132 



Beport of the Council to the 



xxxvn. 4, 



A88et43 and present property of the Society, January i, 1877 • — 



Balance at Bankers*, Bee 31, 1876 ... 
Due on account of Subscriptions : — 

2 contributions of 5 years' standing 

2 „ 4 

II M 3 

22 „ 2 

69 » I 

2 admission fees ... 
2 first contributions 
One amount of ... 



If 



)» 



» 



If 



Balances in hand : — 

In hand of Secretary of Library Committee on 

account of Library Expenses 

Do. do. on account of Tumor Fund 



£ s. 


d. 


£ 9. d. 
238 I 10 


21 







16 16 







69 6 







92 8 







144 18 







4 4 







2 2 







5 5 





355 19 


13 8 


6 




22 3 


9 





35 12 3 
Less amount due to Assistant Secretary on Petty 

Gash Account, Dec. 31, 1876 2 18 8 



£5,200 New 3 per Cent. Consols, including Mrs. Jackson-Gwilt's 

Gift (£300). 
£6,200 Consols, including the Lee Fund (£300), the Tumor Fund 

(£450), and the Horrox Memorial Fund (£100). 
Unsold Publications of the Society. 
Various Astronomical Instruments, Books, Prints, &c 
Two Gold Medals in Stock. 
Balance of Tumor Fund, included in Treasurer's Account, 

£129. $8, 6d. 



32 13 7 



Stock in hand of volumes of the Monthly Notices : — 



Vol. 


At Society's 
Booms. 


At Willlamfl Ac 
Norgate'8. 


j Vol. 

1 


At Society's 
Booms. 


AtWUllamsft 
Korgnte'g. 


I. 


89 


3 


XIV. 


"3 


3 


n. 


90 


3 


XV. 


118 


2 


m. 


• • • 


*• . 


XVI. 


116 


3 


IV. 


• • • 


••• 


XVIL 


142 


I 


V. 


• •• 


••• 


xvni. 


171 


I 


VL 


55 


I 


XIX. 


76 


••• 


vn. 


3 


••• 


XX. 


45 


••• 


vui. 


138 


2 


XXI. 


28 


■•• 


IX. 


19 


I 


xxn. 


44 


••• 


X. 


182 


2 


XXIII. 


28 


••• 


XI. 


190 


2 


XXIV. 


30 


•■• 


xn. 


16 


2 


XXV. 


10 


«• • 


XIII. 


167 


3 


XXVI. 


18 


. .• 



felx 1877. Fifty'SeverUh Aii/nual Oeneral Meeting. 



n^ 



Vol 


AtSodetj's 
SoomB. 


AtWil]iam8& 
Norgate'8. 


Vd. 


At Sooletj'B 
Booms. 


At Williams Ac 
NorgAto^s. 


1 XXVIL 


2 


• • • 


7:7:7:111. 


136 


4 


I xxvm. 


82 


2 


XXTOV. 


108 


4 


\ 3XIX. 


68 


2 


7CXXV. 


36 


4 


I X33L 


78 


4 


7CXXVI. 


71 


2 


I XXXL 


118 

ISO 


I 
4 


Index to'l 
Monthly \ 
Notices J 


612 


I 



In addition to the stock in hand of the volnmes of the Monthly 
Ki^, there are also a considerable number of separate numbers 
of almost every volume. These back numbers, although no com- 
plete Tolume can be formed from them, except of Vol. XXXYI., 
1(6 available for the completion of sets. 

Besides the seventy-one bound copies of Vol. XXXYI., a 
large number of each part are also in stock. 

Stock in hand of volumes of the Memoirs : — 



VoL 


At Society's 


AtWiUiamsAc 


Vol 


At Sodety*s 


AtWiniamsA 


LPwti 


Booms. 


Noxgate's. 


Booms. 


Norgate's. 


3 




7CV. 


153 


I 


LPart2 


50 




XVI. 


182 


• ■ • 


UPtrti 


61 




XVII. 


159 


4 


Q.Ptot2 


26 




xvm. 


161 


I 


mPitfti 


76 




XIX. 


168 


I 


HI. Part 2 


95 




70C. 


164 


I 


IV.Parti 


90 


3 


XXI. Part I 


314 


• •• 


IV.Ptet2 


100 


3 


7CXI.Part2 


99 


• • • 


V. 


"S 


.4 


X7U. 1&2 


70 


I 


VL 


13s 


4 


(together) 
XXU. 


166 


••• 


VIL 


159 


3 


XXTIT. 


162 


I 


vin. 


138 


3 


X7CIV. 


167 


2 


DC 


146 


3 


7LXV. 


180 


2 


X. 


157 


I 


7CXVI. 


183 


2 


XL 


166 


I 


xxvn. 


437 


I 


xa 


170 


••• 


Tcxvni. 


400 


2 


xni. 


184 


2 


2CXIX. 


426 


I 


XIV. 


381 


3 


XTCX. 


176 


... 



134 



Beport of the OouncU to the 



xxxm. 4, 



Vd. 


AtSodety'B 
Booma. 


At Williamfl k 
Norgate*8 


VoL 


AtSooietj'8 
Booms. 


AtWimuns^l 
Norgato'B 


}:;cxi. 

xxxn. 

xxxm. 

XXXIV. 
XXXV. 

XXXVL 

(with M.N.) 

XXXVL 
(without) 

XXXVIL 

Partx 


159 
181 

183 
149 

133 
212 

18 

381 


2 
2 
I 

36 

2 

5 

•« . 

8 


33XVTT. 

Parta 

xx3:viiT. 

XXJUX. 

Parti 

XXXJLX. 

Parta 

XL. 
XLIT. 

Index to 
Memoirs 


329 

327 
313 

333 

389 
404 

707 


• 

5 

2 
3 

I 

3 

4 

5 



Since the last anniversary meeting the Assistant Secretaiy 
has examined the stock of yolames of the Memoirs and Monthly 
Notices mth the greatest care, and he has re-arranged it in a more 
convenient manner for fntnre examinations. In doing this he has 
found several mistakes in the lettering of the different parcels, 
which account for some discrepancies between the lists in thia 
and the preceding Report. 



Instruments helongiiig to the Society, 

The following is a complete list of the instruments belonging 
to the Society. The Council have to regret that most of those 
missing at the date of the last Report are still unaccounted for. 
It is possible, however, that a few of them may ultimately be 
traced, and in consequence it would be unadvisable at present to 
strike them out of the list. 

The resolution of the Council " that the Secret^iries in every 
November shall go through the list of the Society's instruments, 
and send to each person to whom any instrument belon^ng to 
the Society has been lent, a circular desiring him to return the 
instrument to the Society's rooms before the following January 
meeting, or to make a fresh application for it," has been faith- 
fully carried ont. By thus confining the loan of the instruments 
to one year, subject to renewal if required for a longer period, it 
is expected that any unexplained loss of instruments will be 
prevented for the future. The Council have no desire to hasten 
the return of an instrument when it is still of service to the 
borrower, but it is very desirable that it should be returned to the 
Society's rooms as soon as possible when no longer required. 

Some interesting notes by Mr. Lecky on several of the 
instruments may be found on pp. 132-134 of the last Annual 
Report. The complete list is as follows : — 



)} 
n 
n 
n 






it 



Feb. 1877. Fifty'Seventh Annual Oenercd Meeting, 135 

No. I. The Harrison clock, 

2. The (hoen portable circles, by Jones, 

3. The Beaufoy circle, 

4. The BeoMfoy transit instniment, 

5. The Herschelia/n 7-foot telescope, 

6. The Oreig nniversal instniment, by Beichenbach and 
Ertel. The transit telescope, by TJltzschneider and 
Frannhofer, of Munich, 

7. The Smeaion eqnatoreal, 

8. The 0aA)endi8h apparatus, 
„ 9. The 7-foot Gregorian telescope (late Mr. Shear- 
man's), 

10. The Variation transit instrument (late Mr. Shear- 
man's), 

11. The Uniyersal quadrant, by Abraham Sharp, 

12. The ^Z26r theodolite, 

13. The Standard scale, by Troughton and Simms, 
„ 14. The Bea/ufoy clock. No. i, 
„ 15. The Beaufoy clock. No. 2, 
„ 16. The Wollaskm telescope, 
n 17. The Lee circle, 
„ 18. The Sharpe reflecting circle, 
„ 19. The Brisbane circle, 

20. The Baker universal equatoreal, 

21. The Beade transit, 

22. The Matthew equatoreal, by Cooke, 

23. The MaMhew transit instnunent, 

24. The South transit instrument, 

25. A Quadrant, by Bird (formerly belonging to Captain 
Cook), 

)) 26. A Globe showing the Precession of the Equinoxes. 

The Sheepshanks collection : — 

)i 27. (i.) 30-inch transit instrument, by Simms, with 
level and two iron stands. 

a 28. (2.) 6-inch transit theodolite, with circles divided 
on silver; reading microscopes, both for altitude 
and azimuth ; cross and siding levels ; magnetic 
needle ; plumbline ; portable clamping foot and tripod 
stand. 

M 39. (3.) 4-^0 -inch achromatic telescope, about 5 feet 6 
inches food length ; finder ; rack motion ; two other 
micrometers; one terrestrial and ten astronomical 
eyepieces, applied by means of two adapters, with 
equatoreal stand clock movement. 

n 30. (4.) 3^inch achromatic telescope, with equatoreal 
stand ; double-image micrometer ; one terrestrial 
and three astronomical eyepieces. 

» 31* (5.) 2|-inch achromatic telescope, with stand ; 
one terrestrial and three astronomical eyepieces. 



136 Me^ort of the OouncU to the TXXvxx^ j 

No. 32. (6.) 2|-incli achromaiio teleeoope, about 30 ixxeftas 
focal lengih; one terrestrial and four astronaizucal 
eyepieces. This instrument was lent to the lat^ 
Rev. J. Gape, and is believed to be lost. 



If 
11 



i> 



» 



» 



99 



9> 



33* (7*) 3-foot nayy telescope. 

(8-: 



34. (8.) A transit instrument of 45 inches focal 
length ; with iron stand, and also Ys for fixing to stone 
piers ; two axis levels. 

35. (9.) Repeating theodolite, by Ertel, with folding 
tripod stand. 

36. (10.) 8-inch pillar sextant, by Troughton, divided 
on platinum, with counterpoise stand and artificial 
horizon. 

37. (11.) Portable zenith telescope and stand, af-inch 
apertiure and 26 inches focal length ; lo-inch horisosi- 
tal circle and 8-inch vertical circle, read to 10" by 
two verniers to each circle. 

38. (12.) 1 8-inch Borda repeating circle, by Troughton, 
2^-inch aperture and 24 inches focal leng^ ; the circles 
divided on silver, the horizontal circle being read by 
four verniers, and the vertical oirole by three verniers^ 
each to 10". 

39* ( 1 3*) S«inch vertical repeating circle, with diagonal 
telescope, by Troughton and Simms ; circle divided 
on silver, reading to 10" ; a 5-inch Gude at eye-end 
reading to single minutes ; horizontal circle 9 inches 
diameter in brass, reading to single minutes. 

„ 40. (14.) A set of surveying instruments, consisting of 
a i3-inoh theodolite for horizontal angles only, 
reading to 10" ; two sets of adjusting plates; tripod 
stand with enclosed telescope : a deal box with heavy 
Rtand for theodolite ; a box containing the Y piece of 
level; two large and three small ground-glass bubbles 
divided: a box containing level colHmator, objecU 
gla^s i§-inch diameter and 16 inches focal length; 
micrometer eyepiece, comb, and wires, 

«« 41. (15*) Level collimator with object-glass ij-inch 
diameter and 1 6 inches focal length ; stand, rider-level^ 
and fittings. 

,, 42. (16.) lo-inch Tvfiecting circle, by Troughtoii, read- 
ing by three verniers to so ' : counterpoiae stand ; 
artificial horiion with mefvury ; two tripod stands. 

•• 43* ('7*^ Hassler*8 reflecting circle, by Trongfaton, 
with coamerpoise stand. 

,, 44. (^iS."^ 6-inoh refitvtiwg and repeating circle, by 
Trvmghtvxx and Sinuuis contained in thrve boxes, two 
cMT which form stands. The circle is drvided on silver, 
and is rvad u^ siu^k^ minacet^: two inside arcs divided 
to at^c^* deirrvt^s, 1 nC doc?v>es on each side ; artificial 
and mercnrv. 



Feb. 1877. Fifly-sevenkh Annudl Oeneral Meeting. t37 

No. 45. (19.) 5-inch reflecting and repeating circle, by 

Lenoir, of Paris. 
„ 46. (20.) Reflecting circle, by Jecker, of Paris, 11 

inches in diameter, with one vernier reading to 15''. 
„ 47. (21.) Box sextant ; reflecting plane and level. 
„ 48. (22.) Prismatic compass, by Tronghton and Simms. 
„ 49. (23.) Mountain barometer. 
„ 50. (24.) Prismatic compass, by Thomas Jones, 

monnted with a cylindrical lens. 
I) 51* (25*) Ordinary 4^inch compass with needle. 
„ 52. (26.) Dipping needle, by Robinson. 
n S3' (^70 Compass needle, mounted for variation. 
M 54. (28.) Magnetic intensity needle, by Meyerstein, of 

G^ttingen; a strongly fitted brass box with heavy 

magnet ; filar suspension. 
)i 55* (^9-) ^^ o^ magnetic apparatus. 
n 5^' (30.) Hassler's reflecting circle, by Troughton ; 

a I clinch reflecting and repeating circle, with stand 

and counterpoise, divided on platinum with two 

movable and two fixed indices ; four verniers read- 
ing to 10". 
n 57* (31O Box sextant and glass plane, artificial horizon, 

by Troughton and Simms. 
I) 58. (32.) Plane 2| speculum, artificial horizon, and 

stand. 
» 59* (33 2^inch circular level horizon, by Dollond. 
f) 60. (34.) Artificial horizon, roof, and trough; the 

trough Sjh by 4^ inches. 
» ^^' (35*) ^^^ o^ drawing instruments, consisting of 

6-inch circular protractor and common protractor, 

T-square ; one beam compass. 
M 62. (36.) A pentagraph. 
» 63- (37 A noddy. 
** ^4* (3^-) A small Galilean telescope, with object-glass 

of rock crystal. 

»» ^5* (39O ^iv6 levels. 

n 66. (40.) i8.inch celestial globe. 

n 67. (41.) Varley stand for telescope. 

M 68. (42.) Thermometer. 

»i 69. (43.) Telescope,with the object- glass of rock crystal. 

)} 70. Portable equatoreal stand. 

}) 71. Portable altazimuth tripod. 

M 72. Four polarimeters. 

)) 74. Registering spectroscope, with one large prism. 

» 76. Two five-prism direct-vision spectroscopes. 

M 78. 9^.inch silvered- glass reflector and stand, by Brown- 
ing. 

a 79. Spectroscope. 

I) 80. A small box, containing three square- headed Nicol's 
prisms ; two Babinet*s compensators ; two double- 



138 Beport of the Ooundl to ike xxxyu. 4, 

image prisms ; three Savarts ; one positive eyepiece, 
with Nicol's prism ; one dark wedge. 
No. 81. A back-staff, or Davis' quadrant. 

„ 82. A nocturnal, or star dial. 

„ 83. An early non-achromatic telescope, of about 3 feet 
focal length, in an oak tube made in one piece. The 
words "Samuel Scatliffe, Londini, Fecit," are 
engraved on the draw-tube of the eyepiece. 

„ 84. A Hollis observing chair. 

Nos. 73,'7S, and 77 have been removed from the list by order 
of the Council. 

The following instruments are lent, during the pleasure of 
the Council, to the several parties undermentioned : — 

No. 2. The Owen portable circle. No. i, to Mr. Lecky. 

4. The Becuufoy transit instrument, to the Obuervatoiyy 

Kingston, Canada. 
12. The Fuller theodolite, to the Director of the Sydney 
Observatory. 
„ 22. The Matthew equatoreal, to Mr. Brett. 
„ 78. The 9^inch silvered-glass reflector, to Mr. Neison. 
„ 81. Bams* quadrant, to Mr. Lecky. 

From the Sheepshanks collection : — 

27. No. I, to the Astronomer Boyal. 
31. No. 5, to Mr. Birt. 

34. No. 8, to the Rev. Professor Pritchard. 

35, No. 9, to the Sydney Observatory. 
61. No. 35, 6-inch circular protractor, to Mr. Birt. 
67. No. 41, to the Rev. Professor Pritchard. 
69. No. 43, to Dr. Huggins. 



91 



>» 



9) 
99 
9} 
99 
9» 
99 
99 



The Herschelian 7-foot telescope and the Cavendish apparatus 
wore lent to the Science and Art Department of the Committee 
of Council on Education in April last, for exhibition in the 
Special Loan Collection of Scientific Apparatus, at the South 
Kensington Museum. These instruments have now been re- 
turned to the Society, the Exhibition having been closed in 
December last. 

The following is the list of missing instruments : — 

No. II. Universal quadrant, by Abraham Sharp. 
22. The Eeade transit. 
32. Slieepshanks instrument, No. 6. 

64. 9» 9) „ 38. 

66. „ ,, ,, 40. 

68. „ ,, „ 42. 

71. Portable altazimuth tripod. 



Feb. 1S77. Fifly^seveiUh Annual Oeneral Meeting. 139 



The Ja/nson and Oarrington Bequests. 

During the past year the Treasurer has received the .sum of 
two hnncbed poands from the tmstees of the estate of the late 
Mr. T. C. Janson, formerly a Fellow of our Society, who died in 
1863. This legacy, which became payable on the death of his 
widow, has been added to the Lee Fund, in conformity with the 
wiahes of the testator. 

The interest which our late Fellow, Mr. B. G. Garrington, took 
in the welBure of our Society and in the promotion of practical 
as^Domy, remained to the last, although in his later days iU- 
heilth prevented him in a great measure from continuing his 
ftciiye services in the cause of our science. By his will, drawn 
up a few months before his death, he bequeathed to the general 
mnd of the Society the munificent legacy of 2,oooZ. Consolidated 
Annnities, free of duty, which was transferred by his repre- 
lentatives to the Society's Consols account in December last. 
Valued at 94 per cent., the market price on the day of laransfer, 
the amoant crodited to the Society in the Treasurer's Beport is 



The Lihrwry. 

On reference to the Treasurer's Beport, the Fellows will per- 
oeive that the Council has devoted a considerable sum during 
the past year towards the improvement of the condition of the 
library. The principal item of expenditure has been incurred on 
•ccount of the large amoant of binding required to be done for 
the orderly arrangement of the books, more especially of the 
■erial publications. Hitherto, owing to the usual practice of not 
brndin^ most of the serials, and to the confined space devoted 
to the Library at Somerset House, it was scarcely possible to 
preserve that order in the classification of subjects which ought 
to exist in such a valuable collection of astronomical and other 
scientific works as that belonging to the Society, and many of 
the advantages to be derived from a free circulation of the books 
were consequently lost to the Fellows. This was particularly 
felt in the case of the Transactions of foreign academies, and in 
the nnmerous scientific serials, which were often not easily found 
when required. On the removal of the Society to Burlington' 
Bouse, one of the early acts of the Council was the appointment 
of a Sub- Committee, with full authority to reorganise the Library, 
and to devise the necessary measures for placing it in an efficient 
Condition. A liberal sum was at once voted by the Council 
^ defray the expense of binding those works which immediately 
'Quired it for their preservation, and farther grants for the same 
P^irpose have been continued at intervals. 

There is still a large amonnt of binding necessary before 



140 Report of the Ootmcil to the XXXYIL 4, 

the ftill improyement in the Library arrangements will be 
seen, but a cursory glance over the various classified shelves is 
sufficient to exhibit tne satisfactory transformation made in this 
important section of the Society's operations. The attention of 
the Sub-Committee has also been directed to the numerous 
lacuncB in the sets of serial publications, and fortunately they 
have succeeded in filling up many of them ; but there is stiU 
much more to be done in this direction, as it is a notable fBcb 
that the library does not contain a perfect set of the AstronomiBche 
Nachrichten, and some other astronomical serials which are con- 
tinually required for reference. A large number of valuable 
works have been added during the year from various sources. 
Besides the usual amount of presents received, the librarv has 
been enriched by extensive purchases through the Tumor Fund, 
which had accumulated in February last to 164Z. ; by the muni- 
ficent gift from the representative of our late honorary member. 
Miss Sheepshanks ; by Lord Lindsay's presentation of four foHo 
and ten quarto manuscript volumes of Mr. Garrington's observa- 
tions of Sun-spots; by the Rev. F. Hewlett's present of five 
large volumes of drawings of Sun-spots made by him in the 
course of the preceding seventeen years ; and by Mrs. Selwyn's 
gift of a series of paper prints from the solar negatives of the 
Sun taken at Ely in the years 1863- 1873, under the superin- 
tendence of the late Professor Selwyn. 

As the result of the greater facilities a£fbrded to the Fellows 
by the present arrangement of the Library, the Council are' gra- 
tified in being able to report that the circulation of books during 
the past year is considerably in excess of that of former years. 

The general rules and regulations for the management of the 
Library, drawn up by the Council in 1837, having become practi- 
cally obsolete and unknown to the majority of the Fellows, new 
regulations have been prepared with great care in the interests 
both of the Society and of the Fellows. It is hoped that those 
who are in the habit of consulting the books in the Library will 
assist the Council in carrying these rules out in their strict in- 
tegrity. For the convenience and information of the Fellows the 
iiew regulations are inserted below. 



Begulaiums for the Library, 

I. A book shall be kept in which shall be entered the title of 
every book borrowed, the name of the Fellow borrowing the 
same, and the date on which it is lent ; and that an acknow- 
ledgment in writing shall be given at the time of borrowing any 
book from the Library ; and on the return of such book the 
Assistant Secretanr shall insert opposite to the entry the date on 
which the book has been returned, and give in writing an 
acknowledgment of its return. And if, ou the return of such 
book, the Assistant Secretary shall perceive that it has sustained 



Feb. 1877. Fifty-seventh Annual Oeneral Meeting, 14! 

any damage daring its loan, he shall make a note of the par- 
ticnlars, and report the same to the Library Committee. 

n. No book shall be lent before its presentation to the Society 
shall have been annonnced at one of the ordinary meetings, 
udess the President or either of the Secretaries give permission 
to that effect. 

ni. A list of books and periodicals, which are not to be taken 
<mt of the Library without special permission from the Council, 
Bhall be placed in a conspicuous position in the Library. 

17. No Fellow shall be permitted to have more than ten 
. Tolmnes from the Library in his possession at any time without 
Bpedal permission from the Council. 

y. In case any book borrowed from the Library shall be lost 
or damaged, the Fellow by whom it was borrowed shall be held 
nsponsible for the loss or damage ; and, if belonging to any set, 
iUlbe held liable to make good the set to the satis&ction of the 
OoonciL 
YI. All books shall be returned to the Library on or before 
second Friday in November in each year. It shall be the 
duty of the Assistant Secretaiy, before the November meeting, to 
&irward to all Fellows of the Society who, according to the 
o&tries in the book kept for that purpose, have any books belong, 
ing to the Society in their possession, a letter requesting that all 
BQch books be returned to the Society on or before the day of the 
I^ovember meeting. 

Vn. If any Fellow signify to the Assistant Secretary that he 
'eqaires a book already taken out from the Library, it shall be 
^ duty of the Assistant Secretary to make application to the 
FeUow who has borrowed it, and he shall return it, &ee of 
Bxpenae, within a month from the day on which application was 
iBide for it by the Assistant Secretary. 

VIII. Every Fellow who shall have transgressed any of the 
*kve regulations shall be precluded from borrowing any book 
from the Library until he receives the special permission of the 
Council. 

IX. No person who is not a Fellow of the Society shall be 
pwniitted to borrow any book, or to have access to thfl Library, 
^tboQt permission in writing ^m the President or one of the 
SecretBuies. 



FvhUcabiona of the Society, 

Tolnme XLI. of the Memoirs^ containing collected accounts of 
pysical observations of total eclipses of the Sun, which has now 
won upwards of five years in preparation, will, the Council have 
'^won to hope, shortly be in the hands of the Fellows. A copy 
p^ inconsiderable portion of the volume which is already printed 
■ placed in the Library, where it may be consulted by anyone 
mterosted in the sul^ect. The volume will contain a large 



142 Btport of the OownciL to the xxzyn. 4, 

amonnt of claBsified information relating to solar edipaes oIk 
served down to 1874. It will extend to about 600 pages, and 
will be illustrated by woodcuts, and seventeen quarto plates, 
eight of which are devoted to the illustration, on a large soak, 
of the coronal structure visible in the photographs of the ecUpsc 
of December 11, 187 1. 

Nearly all the communications to the Society during the past 
year have been printed in the Monthly Notices^ which still con- 
tinue to be a favourite medium for the early dissemination oi 
astronomical papers. Special attention may be directed to several 
valuable communications by the Astronomer Boyal, the results d 
the extra-meridional work at the Boyal Observatory. The most 
important of these contains the results of the recent observations ol 
the displacement of the lines in the spectra of the stars and planets, 
with the object of determining the motions of certain stars and 
of VefriAM in the line of sight, and for the rotation of the Sun and 
Jupiter, The method employed by Dr. Huggins has been adopted 
in these observations with some modifications, and his oondusionfl 
have been borne out by the Greenwich observations. An inter- 
esting paper by Professor Langley on the measurement of the 
direct effect of Sun-spots on terrestrial climates, and one by Pro- 
fessor Newcomb, on a hitherto unnoticed apparent inequality in 
the longitude of the Moon, have been communicated to the 
Society and printed in the Monthly Notices, Meaiy other im- 
portant communications have been made to the Society, includo 
ing papers by Mr. Elnobel, Professor Harkness, Mr. Darwin, Mr. 
Knott, and others. 

The volumes of the Memoirs and the separate numbers of the 
Monthly Notices as they appear are distributed to the principal 
public observatories and scientific libraries throughout the 
world at a considerable expense to the Society. Twenty-five 
copies of the Monthly Notices are also forwarded to the Hydro- 
grapher of the Admiralty for gratuitous distribution among the 
different surveying vessels. The Council trust that this liberality 
on the part of the Society in the interests of science, will ensure 
a corresponding interchange of all the scientific publications 
issued by our own Government, as well as by the various home 
and foreign institutions on our &ee distribution list. 

It ought, however, to be remarked here that the usual com* 
plimentary copies of some Government publications, which for 
many years have been presented to the Society, will probably 
be discontinued in conformity with the terms of a recent Treasury 
Minute ; and that if this be the case copies of such a work as the 
Nautical Ahrumac can in fiiture be obtained for our Library only 
by purchase. The question is of slight importance if it referred 
merely to the Na/utical Almcmac, which is published at a small 
charge ; but were this Minute carried out on the plea of economy, 
without some relaxation with respect to more expensive Govern- 
ment scientific publications, such as the Oreenwich Observ{Uiati8j 



Feb. 1877. Fifty-seventh AwnudL Oeneral Meeting. 143 

or the 0(ipe Observatimi^y it wonld be the greatest retrograde step 
in the relatioii of Goyemment to science that has ever occnrred.* 
Some of the Fellows may probably be unaware that the 
Memain of the Society are presented gratuitously to them on ap- 
plication to the Assistant Secretary, at Burlington House, either 
vfj themselyee or their accredited a^nts, within three years of 
1^ date of publication. 



Obituabt. 

The Council regret that they have to record the loss by death 
of the following Fellows during the past year : — 

Honorary Member : — ^Miss Anne Sheepshanks. 

Fellows : — Bear- Admiral A. B. Becher. 
C. H. H. Cheyne, Esq., M.A. 
Lieutenant Cyril Corbet, R.N. 
Thomas Dell, Esq. 
Rev. John Edwards, M.A. 
Charles Lambert, Esq. 
Bey. Robert Middlemist, M.A. 
Rear-Admiral H. C. Otter, C.B. 
G. W. Roberts, Esq. 
Cheyalier Fran9ois de Rosaz. 
Lieut-Colonel Alexander Strange, F.R.S. 
Andrew Yeates, Esq. 

Onr late Honorary Member, Miss Anne Sheepshanks, who 
^ed at an adyanced age a few days before the last anniyersary 
i&eeting, was one of the many patrons of our science whose 
memory will remain associated with the history of astronomy in 
tile nineteenth century. The sister and companion of the late 
Ber. Richard Sheepshanks, of whom she was the senior by fiye 
l^m, she shared tibe interest which he always took in the pro- 
giesB of astronomy, and especicQly in the proceedings of this 
oodety, in the administration of which he had laboured so faith- 
^ and so successfully to within a short period of his death. 
Thn»xigh this admiration of her brother's loye for astronomical 
^ork, and also as a record of her own affection for his memory, 
'Gtt Sheepshanks determined to deyoto a considerable portion of 
'^ propOTty for the promotion of the study of his &yourite 

* It will be graUfying to the Fellows to be informed that since this R^rt 
*** nad at the Annnal Meeting, the Astronomer Royal has received an oD&ial 
^PWnnication from the Secretary of the Treasury, dated Februaiy 9, 1877, 
!^ng that the Stationery Office has been authorised to hand over the whole 
^"iptMon of the Greenwich Observations eyerj year for gratuitous distribution 
Monrdiog to the discretion of the Astronomer Royal, subject only to an annual 
^port of the details of the distribution being submitted to the Treasury. — 



244 Beport of the OouncU to the 

Rcience in the University of Cambridge. To carry out her 
in the most advantageous manner, she sought the advioe au«} 
assistance of some of her brother's most intimate scientific friend^ 
by whom she was guided in her decision as to the appropriatum 
of her intended gift. She ultimately resolved to transfer the 
munificent donation of io,oooZ. Consols into the joint names of 
the Master, Fellows, and Scholars of Trinify College and Mr. 
(now Sir George B.) Airy, the interest of which was to be devoted 
to the advancement of astronomical and kindred sciences in the 
University. A Grace, accepting the gifb, was passed by the 
Senate at the Congregation held on the 9th of December, i8c8. 
It was finally recommended by Dr. Whewell, Master of Trinity 
College, and Mr. Airy, on the part of Miss Sheepshanks, mud 
agreed to by the Vice-Chancellor and other University authori- 
ties, that one-sixth part of the amount, producing 50Z. per 
annum, should be specially devoted to the foundation of an asta>» 
nomical scholarship at Trinity College, to be named the " Sheep- 
shanks Exhibition,'' and that it should be open to the nnder- 
graduates of any of the colleges, the exhibition being awarded, 
after examination, to the candidate best versed in theoretical and 

Sractical astronomy. Bearing in mind the long connection of 
[r. Sheepshanks with Trinity College as one of its Fellows, it 
was considered that the endowment of this permanent astrono- 
mical exhibition would be a most appropriate memorial to him in 
his own University, and at the same time be subject to the cars 
of his own College. Though the Sheepshanks Exhibition is 
open to the whole University, it has been practically confined to 
Trinity College, and it has been generally given to one of ite 
undergraduates, who subsequently attained the high position of 
senior wrangler. The first examination took place in 1859. The 
exhibition is tenable for three years, on condition that the bolder 
shall keep, by residence, every University term during that time. 
The interest of the remaining five-sixths of the donation has been 
reserved to be applied, as required, for the promotion of astro- 
nomv, tem.«trial magnetism, and meteorology, in connection with 
the Cambridge Obeervatonr, either in the payment of the stipends 
of the assistants and computers, or in the purchase of instromentB. 
In iSoo, an additional sum of 2,000/. was placed by Miss 
Sheenshauks into the hands of Mr. Airy to provide a fond 
for tW puivhaso of a new transit-circle for the Cambridge 
Obeerratonr. Ciivumstances liaving prevented the immediate 
ennnion of the instrument, Mr. Airy, with the donors consent, 
tranatt>mxi the amounts with its aocuniulated interest, to the 
Viiv-Chancv^llor in the Uyinningof 1S63, ^ Grace having 
the Senate for its ao^vpiance on the lith of March of tl»t 
Fi\>m this skWMid aiM of Ivnofiivn^v on the pan of Miss S&eep. 
shank^fk fho Cambridj^^ Ohsor\T»tory hsis Kvn enriched by the 
excellent meridisw-^^in^lo, whioh \^Tis ^vnstraoted by Mr. James 
Simnis, and mouiiuxi in the l.»*ttor }ian of 1S70. ' It is a firat- 
ck» meridional instruments and oompaxv« tavoujn&bly with those 



Teb. 1877. Fifly-aevenih AnmuU Ghn&ral Meeting. 145 

at other public obeer^atories. It is furnished with an object- 
glass of eight inches apertnre, and is provided with two 
graduated drdeB of three feet in diameter, one fixed and the 
other moYable. It has also two collimating telescopes, as in the 
Greenwich transit-circle, each of six inches apertnre, which can 
be directed on each other through the central cube of the instm- 
ment In its construction generally, advantage has been taken 
of many recent improvements in this class of instruments. 

Miss Sheepshanks, after the sudden death of her brother 
in 1855, lived a very retired life at her residence at Reading, 
ikreshe died on February 8, 1876, aged eighty-six years. The 
fellows of the Society are greatly indebted to her representa- 
Ine, the Bev. Thomas Sheepshanks, for his spontaneons and 
nhable donation to our Library of 161 separate works, consisting 
0(192 volumes, forming a portion of the library of the late Bev. 
K^ard Sheepshanks. Many of these works are extremely rare, 
ad of considerable pecuniary valne. The title of each work 
Wf be found in the fist of presents attached to the supplementary 
nmber of Vol. XXXVI. of the Monthly Notices, A box containing 
ihi]g8 number of letters on scientific snbjects, received by Mr. 
Sheepshanks from several distinguished astronomers, together 
^ other correspondence on some controversial matters, has 
ibo been presented to the Society, at the request of the Secre- 
iuies. These have been sorted and arranged, and it is the 
intention of the Council to have them bound in an orderly 
ffiumer for easy reference. b. d. 

Bear-Admiral Alexandbs Bbidpobt BECHlfB was the son of 
C^Ham A. Becher, B.N., an officer of high scientific attainments. 
Hie was bom in tiie year 1796. He entered the Boyal Naval 
College in 18 10, and in November 181 2 he joined the Barharrif 
74* Captain Spanger, with whom he served as master's mate. 
This snip was attached to the Channel Fleet, then engaged in 
ibe htockade of Brest, from which it was detached to take a 
Itrge conyoy of ships to and from the West Indies. Affcer 
MiTinga short time in the Oordelia^ a lo-gun brig, in the Channel, 
lie joined Commodore Owen for active service on the lakes ol 
Osnada during the American War ; bnt on peace taking place 
ioon afterwards, he was transferred to the surveying party 
nnder the command of Captain W. F. Owen, brother of the Com- 
modore. This officer was in 18 15 commissioned to survey the 
CSaoadian Lakes and the Biver St. Lawrence. Yonn^ Becher 
entered heartily into this work, for which he was exactly suited, 
Uie survey having been carried on by a large party afloat in 
tammer, and on the ice in winter, and he has remarked that 
** he took his full share of the ice work, and had as many duck* 
ingB from breaking through the ice as anyone of the party." 
In 1818 he joined the Sv^perh^ 74, at Plymouth, and in Sep- 
tember of that year the Leven^ Captain Bartholomew, with 



146 Report of the Oounoil to the XXXTU. 4 

whom be spent twenty months on scientific service in thi 
Atlantic, determining the longitude of Fonohal, rock hunting 
and in surveying the Azores, a part of the African coast, and somi 
of the Gape Verd islands. In 1820 he was appointed to tin 
Conway^ 26, Captain Basil Hall, on the South American station 
and in May 1822 he received his first promotion, as Lieutenant 
Between March and December 1839, ^® served as First Lien 
tenant in the Favty^ surveying vessel, which in the followini 
year foundered during a severe gale in the North Sea^ witi 
the loss of Captain Hewett and all his crew. He was mad 
a Commander in 1841, and his last service afloat was undertake] 
in 1848, to qualify himself for promotion to the next step o 
rank. Captain Becher thus completed his necessary perioc 
of active service as Commander of a surveying vessel on thi 
coast of Scotland. In 1856, he attained the rank of Captain 01 
the Reserved list, and about a year before his death that o 
Retired Rear. Admiral. 

In 1837, Lieutenant Becher communicated to the Society] 
description of his well-known pendulum artificial horizon, to b 
attached to a sextant or quadrant for the purpose of observing 
altitudes by day or night at sea. The special object of the in. 
vention was to provide a means of making accurate sextan) 
observations when the real horizon is invisible, either from haze 
fog, or other causes. This practical instrument, the result oJ 
Lieutenant Becher's nautical skill, requires careful management 
and when used by competent observers, it has been proved to bi 
a valuable aid to the nautical astronomer. This extra can 
required has prevented it from becoming generally adopted ii 
the Service ; but the Admiralty acknowledged the ingenuity a 
the inventor by granting him a moderate pecuniary reivard. 

In 1823, soon after his return from the South Amerioai 
station, an opportunity was afforded him of employment at Um 
Hydrographic Office. Owing to the recent death of the Hydro 
grapher, an officer was required to arrange and methodise, fen 
easy reference, all the numerous suid varied documents preservec 
in that office, consisting of charts, maps, and plans of every kind 
both printed and in manuscript. This entailed the compilatioi 
of a general and alphabetical catalogue, with a methodical geo- 
graphical arrangement of the whole of the papers. For sad 
a work Lieutenant Becher, who happened to be visiting the 
Admiralty with the object of obtaining an appointment in anothei 
ship, appeared to be just the person required; and as he had 
been accustomed to maritime surveying, and was well acquainted 
with the construction of charts, this duty was offered to him bj 
the new Hydrographer. He very gladly accepted the laborioiu 
task ; and his youth and vigour, together with a natural love foi 
the seaman's chart, and a zeal that would not yield to anj 
amount of work, carried him on to the completion of the 
catalogue, which required three years for its performance. The 
number of separate entries exceeded 50,000. 



Eeb. 1877. Fiftysevenih AwmmI OenercU Meeting. 147 

Lieateiiant Beoher's experience of marine soryeying, and his 

eeneral knowledge of hjdrographio work, increased in no small 

degree bj his recent duties, led to his permanent appointment as 

instant in the Hydrographic Office, in which he remained till 

lus retirement on superannuation in 1865. Twice during this 

kog service he was permitted to go afloat to qualify for rank ; 

to his Admiralty employment was, in each case, kept open for 

Inm till his return. While holding the official rank of Chief 

Anstant to the Hydrographer, Captain Becher also acted as 

neretaay to the Bc^urd of Visitors of the Boyal Observatory. 

At the annual visitation on the first Saturday in June of each 

yeir, it was his invariable custom to give an official character to 

Us journey from the Admiralty, and many will recollect the 

pieuant hour passed in his company from Whitehall to Oreen- 

lieh in the Admiralty barge. He became a Fellow of the Royal 

Aitatmomical Society in 1830, and has served on the Council. 

Captain Becher took a great personal interest in the success 
of the N<PuHcal Magaziney of which he was the editor from its 
oomiDencement in 1832 to 187 1. It was his chief endeavour to 
nab it a &vourite among nautical men, in which they might 
^ bydroeraphical notices of the discoveries of rocks and shoals, 
tk establi^mient of light-houses or buoys, and of all matters of 
interest relating to the Navy or the Mercantile Marine. It was, 
indeed, a child of his own. He was its guiding spirit during the 
forty years of his editorship, and he succeeded in obtaining for 
it a considerable professional reputation, its pages having been 
always open to the advocacy of any cause which had for its 
obje^ the promotion of the interests of naval officers, or the 
uielioration of the condition of our seamen. Many of the most 
nnportant papers in the Magazine were from his own pen, in- 
<Mng translations of foreign hydrographical notices. Captain 
ftcber was often occupied in his leisure hours with other literary 
^ork ; and in his Landfall of Golumbtbs he has apparently suc- 
QKded, after much labour, in tracing the actual progress of 
Oohmbus among the islands discovered by that great navigator 
^ his way to Cuba. 

During the last few years of Admiral Becher^s life, failing 
Mih compelled him to relinquish all public work ; and he lived 
ni retirement, respected by the profession as a kind friend, a 
^•lons and hard-working officer, and a valuable public servant, 
ffij promotion to the rank of Rear- Admiral was gratifying to 
^ m his old age, though he did not long enjoy the nonour. 
^ died at his residence in London on the isth of February, 
JJ76, in his eightieth year. His daughter is the wife of Dr. 

cott. Bishop of Gloucester and Bristol. b. d. 



Charles Habtwell Horne Chetne, M.A., was the eldest son 
^ the Rev. Charles Cheyne, many years Second Master at 
(j^^'b Hoi^ital, and maternal grandson of the Rev. T. Hartwell 

M 2 



148 Report of ike Council io the xxx?iu ^ 

Home, the well-known Commentator. He was bom on t^lia 
isfc of Maj, 1838, and was educated at Merchant Taylors' Sohoa/, 
where he oontinned till he entered St. John's College, Cambrid^ 
in October 1857. He was elected to a foundation scholarfihip 
at that college in Jane 1859, and obtained the B.A. degree in 
January 1 86 1, as eighteenth wrangler in the Mathematical Tripos. 

Soon after taking his degree, Mr. Cheyne contributed to the 
Quarterly Journal of MathemcUics, and to the Messenger of 
Maihematicsy three original articles on the variation of ihe E1^ 
ments in the Planetary Theory. These were followed in October 
1862 by the publication of his Elementary Treatise on the Plane^ 
tary Theory, which includes his own investigations, besides all 
that is important to the student from the works of former writers 
on the subject. This systematic treatise has become the re* 
cognised text-book in Cambridge, and has reached a seoond 
edition. Subsequently, in September 1867, Mr. Cheyne pub- 
lished an essay on the EartWs Motion of Rotation. In the first 
part of this work he developed the aiudogy between the pro- 
cesses for obtaining formulsB for the variation of the elements 
in the two problems of the Earth's motions of translation and 
rotation. The methods of investigation are remarkably original, 
and the subject was presented, for the first time, to English 
students. The second part contains the application to the 
questions of Precession and Nutation, and the stability of the 
E]arth's rotation. 

In March 1863, Mr. Cheyne was appointed Second Mathe- 
matical Master of Westminster School, and in 1864 he proceeded 
to the M.A. degree. While at Westminster, he published, in 
conjunction with his colleague, the Rev. C. A. Jones, a collection 
of Algebraical Exercises, progressively arranged, a work whioh 
has passed through several editions, and is largely used in onr 
Public Schools. In June 1868, he was elected a Fellow of onr 
Society, and he was a frequent attendant at our meetings. "nTM 
singfularly quiet and unobtrusive disposition prevented him from 
taUng any active part in the proceedings of the Society, fir 
which he was so well qualified ; and the pressure of his school 
duties legitimately interfered with any desire he may have 
entertained for continuing his astronomical researches. 

For the last two years Mr. Cheyne had been in failing health, 
which ultimately compelled him to resign his mastership in the 
school. He, however, retained his position there till only a few 
weeks before his death. He retired to the milder climate of 
Torquay, where it was hoped that his health would be at least 
partially restored; but the change was made too late, and he 
sank from exhaustion within a fortnight of his departure from 
Westminster, on the ist of January 1877, at the early age of 
thirty-eight. 

Lieutenant Ctril Corbet, R.N., was bom at Shrewsbniy on 
the 24th of March 1850. He was the youngest of ten childien 



Feb. 1877. ISfty-aeventh Annual General Meeting. 149 

of Mr. Philip Corbet. At the early age of seven he was Bent 

to Christ's Hospital School, and at twelve he competed for and 

guned the first cadetship offered to the school by the Board of 

Admiralty. He entered the Royal Naval College at Portsmouth 

i& December 1862, becoming a midshipman in March 1864, 

iben he joined the Prince Consort^ Captain Willes. In Decem- 

W 1869, while serving in the Fallas, he was made a Sub- 

Ufinteiuuit^ and in the same year he gained the " Beaufort 

TeBtimoniaJ," awarded to the officer who obtained the highest 

nmber of marks in the examinations of the year. In March 

1870, he was appointed to the Zealous, flag-ship in the Pacific, 

ndon the 30th of December 1872, he was gazetted Lieutenant. 

WkUe serving in this ship his natural geniality and kindness of 

dspofiition made him a great favourite with both officers and 

WD. The record of many of the incidents of their three years' 

cniie along the American shores and islands in the Pacific has 

ippetred in Our Journal in the Pacific, to which Lieutenant 

Oorbet made several contributions, more especially the chapter 

nbting to an interesting adventure in the wilds of British 

Gofaunbia. 

On the return of the Zealous to England in 1873, Lieutenant 

Corbet was requested by the Admiralty to join a select number 

of officers who had volunteered for service in connection with 

tbe observation of the Transit of Venus in December of the 

following year. He most willingly accepted this duty, and, in 

oonaequence, he proceeded to the Boyal Observatory to receive 

tiie Decessary instruction in the use of the various instruments 

i^niied for the observations. Into this preliminary work he 

ntered with the utmost energy and zecd, and soon became 

practically conversant with thd methods of making and reducing 

the observations. His steady attention to his duties at the 

Obeerratory was the cause of his selection for the important post 

€i chief observer at the second station in Kerguelen Island. 

For a position of trust of this nature, his high principle, and 

Mmest, thoughtful, and devoted character peculiarly fitted him. 

fie was fully convinced of the importance of this charge, and 

dninff his leisure hours at the Boyal Naval College at Green- 

'wich he was ever improving his acquaintance with the theory 

of the observations which he would be required to make at his 

dirtant station. 

In addition to the appointment as chief observer at the 
second Kerguelen Station, Lieutenant Corbet was also entrusted 
with the care of the chronometers especially employed for 
determining the difference of longitude between the Cape 
Ofaiervatory and Kerguelen, and for the connection of the 
vmrions stations in the South Indian Ocean. Sailing from 
England for the Cape of Good Hope in May 1874, in charge of 
the first detachment of observers, he was ever at work throughout 
the voyage, as well as during his stay at the Cape, perfecting 
himself in calculations and observations, or superiutendiug the 



150 BepoH of the Council to the xxxvn. 4, 

necessary preparations in the dockyard at Simons Bay. Hb 
appeared to throw his whole soul into the duties he had nnder- 
taken, and his persevering and oheerfal labonr was a great 
enconraeement to others, as well as being most yalnable in itadU. 

On me day of the transit he was fortunate in obtaininff an 
accurate observation of the first internal contact, the mhA 
light streak around Venus being in perfect contact with the 
Sun's limb; but clouds prevented observations at the egrev. 
The first two months in Kerguelen were devoted exclusively to 
the necessary preparations for the important obseiVationB on 
December 8 ; but during the remainder of his stay in the island 
he spent many nights in taking his bum at the transit or alt- 
azimuth instruments, while the chronometer-runs and longitude 
calculations well filled up his days. Even on his homewaxd 
journey he continued his work, and it was only when he received 
at Bombay the sad intelligence of the death of his mother, that 
he was afc last forced to discontinue his calculations and to 
return in all haste to England. 

In June 1875, Lieutenant Corbet was appointed to the BiruUf 
commissioned for service on the West Coast of Africa. Having 
been sent to visit the G-ovemor of the Colony at Loando, he was 
struck down on the following day by coast fever. He was ai 
once taken to St. Helena, where he died, soon after reaching that 
island, on the 17th of February 1876. Thus suddenly closed a 
career full of promise, before he had completed his twenty-sixUi 
vear. Honoured and beloved by his fellow-officers and men, tbl^ 
have placed a monument over his remains, as a tribute to bu 
memory, in the cemetery of St. Helena. 

Lieutenant Corbet was elected a Fellow of the Royal Astro- 
nomical Society on December 10, 1875, little more than two 
months before his decease. His connection with us was, there- 
fore, of very short duration. The announcement of his premature 
and sudden death was deeply deplored by his many friends. The 
simple thoroughness and kindliness of his nature caused him to 
be highly esteemed and beloved by others than his immediate 
relations and private acquaintances, especially by those with 
whom he had been officially associated in the Navy, or in con- 
nection with the Transit of Vejius operations both at Greenwich 
and Kerguelen. 



The Rev. John Edwards, M.A., of St. Aidan's College, 
Birkenhead, was ordained by the Archbishop of York in 1856. 
He was appointed to the rectory of Bradford-cum-Beswiok, 
Manchester, in 1859, which he held till his death. At an early 
age he became mach interested in astronomical science, and, in 
his later years, became thoroughly versed in its history and 
standard writ<.»ra. Frequently he devoted the little leisure at his 
disposal to astronomical observation, which was always a pleasure 
to him. Mr. Edwards was a ready and eloquent speaker, and 



Feb. 1 8 77* Fifty^sevetUh Armual General Meeting. ' 151 

ooeasioiiaily lie delivered a series of nstronomioal lectnres, re- 
markable for their simplicity and comprehensiveness. He was 
deoted a Fellow of the Bojal Astronomical Society on Novem- 
W 12, 1869. His literary attainments were highly respectable. 
He had a well cultivated mind, and was intimately acquainted 
wttih biblical literature in general, witli ecclesiastical history, and 
wiih the various controversies of the Church, of all ages. As a 
pixochial clergyman, Mr. Edwards had few equals in the ability 
d hiB ministrations, the ardour of his zeal, and the abundance of 
Ub labours. He possessed naturally great geniality of spirit, and 
VBB singularly affectionate in disposition. His death has there- 
fere been deeply regretted by his clerical brethren, by his 
penonal friends, and by his parishioners. Mr. Edwards died at 
bIs rectory at Bradford-cum-Beswick on the 30th of January 
1S76, at the age of fifty*eight. 

The Bev. Rorebt Middlemist, M. A., was bom on February 29, 
1S08, and was descended from a respectable Northumberland 
&nrily. He was educated principally by his relative, Mr. 
Ooarley, who was at that time H^id Master of the Grammar 
Schools at Morpeth and Hexham. When quite a youth, he was 
in the habit of answering mathematical questions given in the 
l^*s Diary^ by which means he soon became known by 
ume to some of the leading mathematicians of the day, who 
were also contribators to the mathematical section of the Diary. 
By one of these, but an entire stranger to him, he was re- 
commended, in 1831, to Lieutenant Stratford, the Superintendent 
of the Nautical Almanac^ as a highly-qualified computer and a 
good mathematician. This led to his engagement as one of 
■•▼eral young computers required to perform the calculations of 
tko new and enlarged edition of the Nautical Almanac on 
the greatly improved plan adopted in November 1830 by a 
Committee appointed by the Council of the Astronomical 
Society, and afterwards approved by the Lords Commis- 
•onera of the Admiralty. Previous to this, the computations 
of the Nautical Almanac were made in different parts of the 
*^try, three of the computers residing in Cornwall, and 
^w at Greenwich, Ludlow, Tides well, &c. Two only of 
^e old computers, Mr. William Dunkin, of Truro, and Mr. 
Henry Jenkins, of Greenwich, were reiiiined for service in 
the newly-established office. Mr. Middlemist was one of the 
■'■t appointed on the staff, and he was therefore engaged on 
"fi Almanac for 1834, the first of the new series. He was 
Jnch trusted by Lieutenant Stratford, who had great confidence in 
nifl abilities, and he was selected to make the careful comparison 
■nd examination of the duplicate calculations; a duty he per- 
formed with such patience and fidelity, that Lieutenant Stratford, 
in the Pre£Eu;e of the Nautical Almanac for 1834, remarked that it 
wag impossible to appreciate too highly the manner with which 



152 ' Report of the OounoU io the xzxyil 4^ 

he ezecnted this most tedious task. Mr. Middlemist joined otix* 
Society on March 14, 1834. 

After having served for some time as mathematical master 
in the Royal Naval School, Mr. Middlemist entered Christ's 
College, Cambridge, in 1838, as an undergraduate. He became 
a scholar of his college, and graduated as B.A. in January 1842, 
being 27th Wrangler. For a time he acted as curate to the 
Bev. J. E. Ghretton, of Stamford; but in 1845 ^® received the 
important appointment of senior assistant mathematical master 
in Harrow School, an office which he retained till his death. 
He was also vicar of Little Linford, Bucks. Though an ocoa- 
sional attendant at our meetings, Mr. Middlemist does not appear 
of late years to have interested himself much in astronomy, and 
he has never been a contributor to the Proceedings of this SocietT. 
While on a visit to his sister at Bamsgate, he was suddenly 
attacked with inflammation of the lungs, and died there eight 
days afterwards, on the nth of January 1877, in the sixty-ninth 
year of his age. He has left a widow and seven children — siz 
sons and one daughter. e. d. 



Rear.Admiral Hknry Charles Otteb, C.B., was bom in the 
year 1807. At the age of fifteen he entered the Navy as a 
cadet, and obtained his first commission as Lieutenant in 1831. 
From August 1833 to the end of 1835, ^® served as a super- 
numerary Lieutenant in the Oceoti, 80, and Houw, 120, atSheer- 
ness. At this time he gave many indications of his talents as a 
scientific officer, and much of his leisure time was occupied in 
perfectiug himself in astronomical observing, especially with 
those instruments which are practically used for surveying pur- 
poses. His acquaintance with the principal nautical astronomers, 
adtUni to his personal attachment to the observing branch of onr 
sciouoo, induced him to become a Fellow of the Eoyal Astro- 
nomical Society, to which ho was elected on the nth of Novem- 
hoT 1842. In March 1844, Lieutenant Otter was appointed to 
the command of the Sparrow^ surveying vessel on the coast of 
Scotland, and thus commenced that active career as a nautical 
surveyor under the Hydrogrnphic Office, which he continued for 
a long numlH>r of years, commanding in succession the Avan^ 
Porruphit\ Shamnx'kf nnd other sun-eying vessels. 

Admiral Otter, when a midshipman, had the satisfaction of 
performing a most gallant act, as by his heroic exertions he was 
the moans of saving the lives of a boat^s crew while in extreme 
danger, and so latoly as 1845 he jumped overboard from the 
^';»flrl^>fr for the pur|x>se of affording assistance to some of his 
crew who had Ihvu ca|isir.od. Most of his time till his retire- 
ment was six'nt atloat in the performance of his surveying dutiea. 
Uis sucoossivo pn>motion8 were to Commander on August 26, 
1844; to Captj^in on Septomlvr 8. 1S54; and to Retired Bear* 
Admiral ou April 1, 1870. Ue died at Clare Park, Hanta, on 
the 20th of Miuvh 1S70. ai^xl sixty-eight. £• D. 



fA. 1877. lykf'SevefUh Afimud Oeneral Meeting, 153 

OiOBGB Walteb Bobbbts was the third and youngest son of 

the late Air. Heniy Roberts, of Grow Trees, Gomersal, near Leeds, 

where he was bom on Febmarj 9, 1846. From early life he took an 

interest in astronomy, and about the year 1867 he formed a plan 

of making a series of planetary delineations with a 12-mch 

reflector, but he was prevented from carrying out his wishes by 

ibe wanton destruction of his instrument by a party of drunken 

Toughs. He, however, shortly afterwards erected a new Obser- 

nftoiT, which he furnished with a transit instrument, and an 

&*inch achromatic telescope, by Wray, equatoreally mounted. 

?7ith this instrument he was accustomed to devote many of his 

Mmre hours to astronomical work, though he was not usually 

i& the habit of publishing his observations. On March 26, 1873, 

be observed the fourth satellite of Jupiter during its transit across 

ttie planet's disk as a very intensely black spot, the particulars 

ofihe phenomenon being recorded in Vol. XXXIII. of toe Monthly 

^oUces. A recent change of residence, combined with increasing 

iU-health, compelled him to relinquish all scientific work. Mr. 

Boberts, who joined our Society in March 1872, was ever willing 

^ give his assistance in spreading an interest in astronomy in 

^ neighbourhood ; and his cultured mind and genial disposition 

l^iOQght him a lar^ circle of personal friends, by whom his loss 

^ be severely felt. He died at his residence in Leeds, on 

January 19, 1877, in the thirty-first year of his age, leaving a 

^ow and two daughters. 



The Chevalier Fban^ois de Rosaz was a native of Savoy, but 
tbe latter part of his life has been spent in England. He was 
the only son of a gentleman of some position in his native 
country, and was originally educated for the medical profession ; 
hut his tastes inclined to law rather than to medicine, and he 
eventually became, during the reign of Louis Philippe, a suc- 
cessful advocate in the legal Courts of Paris. Having been a 
great supporter of the Orleans dynasty, he resolved to leave 
France aiter the Bevolution, which resulted in his retirement 
altogether from his profession. He now settled permanently in 
England, residing alternately in London and at Brighton, where 
he continued to lead a most active life, devoting nearly his whole 
time to philanthropic objects, even to within a short period of 
bis death. He was the founder or supporter of seven distinct 
charities at Montmelian, his native town, and nearly the whole 
of his large property is ultimately to be reserved for their per- 
manent benefit, and for the foundation of similar charitable insti- 
iations at Brighton. M. de Rosaz was naturally a scientific man, 
and in his leisure hours he was in the habit of making himself 
acquainted with the practical use of many valuable instruments 
wluch he possessed. He was particularly fond of astronomy, 
and on his election less than three years ago, he expressed to one 
of the Secretaries his gratification at being admitted in his old 



154 Report of the Ootmcil to the xxxvn. 4, 

age a Fellow of the Society. His astronomical instruments, 
whicli have been the means of affording instmction to many of 
his friends, are bequeathed to the Mnsenm at Brighton. Hia 
death took place rather suddenly in London, on the 2i8t of 
September 1876, in his seventy-sixth year. B. d. 

Lieutenant-Colonel Alexander Stbange, F.B.S., was bom at 
Westminster on the 27th of April 1818, and was the fourth son 
of Sir Thomas Strange. He received his principal education at 
Harrow. Li 1834, at the early age of sixteen, he was appointed 
to the 7 th Regiment of Madras Light Cavalry, and soon after 
left England for India, where he passed a continued service of 
twenty-six years, a large portion of which was in connection 
with the Great Trigonometrical Survey, then under the superin- 
tendence of Captain (now Major-General Sir Andrew) Waugh. 
His abilities, which were of the highest order, attracted the atten- 
tion of several scientific officers, from whom he received not only 
valuable counsel, but also practical instruction in the use of astro- 
nomical and surveying instruments. His mechanical skill, so 
advantageously utilised in after years in his designs for improved 
geodetical instruments, made it obvious to the military authorities 
that scientiGc employment was his natural avocation, and that his 
talents would prove more advantageous to the service if devoted 
to the scientific branch of the army than if they were permitted 
te remain dormant in the routine performance of his regimental 
duty. For a time he studied at the Magnetic and Meteorological 
Observatory at Simla, then under the charge of Major (now 
Major-General) Boileau, F.B.S., and in 1847 he received the 
appointment of second assistant in the Great Trigonometrical 
Survey, the duties of which exactly corresponded with his taste 
for astronomical observing. He thus obtained a fall scope for the 
exercise of those peculiar talents for scientific work which he had 
exhibited from the time of his entry into the service. 

Soon after the acquisition of Scinde and the Punjab, the 
Surveyor- General considered it of great importance i3iat the 
newly-acquired territory should be connected with the " Gh«at 
Arc Series " of triangulations, having the Dehra Doon base at 
the north, and the Sironj base at the south. From the base at 
Dehra Doon a north-western series was also to be extended to near 
Attock, where a new base was to be measured. It was likewise 
resolved that the line of the " Calcutta Longitudiual Series " 
should be extended from the Sironj base to Kurrachee, to be 
named the " Great Longitudinal Series,'* forming, with extensions 
to other districts of the Indian territory, a perfect gridiron of 
triangulations. The western section of this operation was com* 
menced at the end of 1848 by Captain Kenny (afterwards Major 
Renny-Tailyour), assisted by Captein Strange and others, com- 
mencing from the Sironj base. In the following year, Captain 
Benny retired from the Survey, after having executed about 



Feb. 1877. Fifty-seventh Annual Oeneral Meeting, 155 

eighty miles of triangnlation. He was sacceeded by Captain 
Strange, under whose superintendence this important geodetical 
work was brought to a successful termination. He was assisted 
by Lieutenant (now Colonel) Tennant, B.E., and a civilian staff. 
This triangulation was carried over the rugged range of the 
Aravulli mountains, then across the great Thurr, or desert, to the 
north of the Bunn of Cutch. After crossiog the valley of the 
Indus, the party reached Kurrachee in April 1S53, after five 
seasons of very severe work. Some idea may be formed of the 
magnitude of this great triangulation by a reference to the actual 
distances between the commencing and terminal stations. It has 
been calculated that the series was 668 miles in length, and con- 
sisted of 173 principal triangles, covering an area of 20,323 
miles. This is also the first example of a true desert being 
mooessfolly^traversed by a great triangulation. 

The remarkable energy displayed by Captain Strange in the 
aanagement of this great surveying work reflected on him the 
lugkest credit, and the manner m which the triangulation was 
erocted was fully to the satisfaction of the Surveyor-General. 
How these field duties were performed by the party, and what 
obstacles they had to encounter, is thus related by Mr. Clements 
B. Uarkham, F.B.S., in his Memoi/r on the Lidian Sv/rveys^ a work 
to which the writer is indebted for several of the facts contained 
in this notice. " The great difficulty, peculiar to this series, was 
the crossing of the desert. No geodesical operation of the first 
order bad, at that time, ever been conducted in a desert, and 
experience was therefore totally at fault as to the probable 
obstacles to be encountered. Stations had to be selected, in the 
first instance, by an advanced party. At each station a masonry 
platform had to be erected in a country entirely composed of 
ttnd, and destitute of building materials. After this had been 
accomplished, the main party engaged in taking the final obser- 
vations, numbering two hundred men, had to be maintained in the 
desert during a whole season. The desert furnished only three 
things useful to man or beast, namely, grass, immediately aft;er the 
rainj season ; limited suppUes of milk ; and brackish, or, more cor- 
rectlj, salt water in deep wells, scattered at wide intervals. The 
arrangements therefore involved the sapply of provisions of every 
description for two hundred men during several months. * * * 
Cftptaiu Strange's party reached the borders of Scinde, and com- 
menced operations on the 8th of December 1852. The first station 
was Chortlee, where it was necessary to observe from a tower 
thirty-seven feet high, the side being twenty-two miles long, and 
crossed by the Indus. The view was obstructed by a dense hahool 
jungle, intersected in many places by sheets of water. It was a 
tedious task to clear the line, and then it was long before the 
signal could be made out at the other station of Helaya, twenty- 
two miles away. After a wearisome detention of twenty-five 
da?B, and much painfuL straining of the eyes, occasional faint 
ghmpses cyf Helaya were caught, and at length the angle was 



I 



156 BepoH of the OouncU io the XXXTIL 4, 

satiBSAotorily observed. At the next station of Kanad there 
were fresh misfortunes. The tower, thirty-nine feet high, began 
to emit a cracking sound towards evening, and lucHly the 
ereat theodolite had not been placed, when one of the angles fell 
m. At another place the great theodolite narrowly escaped 
destruction from a hurricane, and was rescued by the desperate 
efforts of its guardians, amidst the war of the tempest, in a night 
of inky darkness. Such are the sort of harassing difficulties and 
delays which form the daily life of the surveyor, but which are 
ever cheerfuUv faced and overcome. Captain Strange and his 
party had their full share ; but at length their work was com- 
pleted, and the last angle of the series was taken at Muggur Peer 
station on the 22nd of April 1853." 

From this time Captain Strange was employed continuously 
on surveying work, and in June 1854 he was promoted to the 
rank of Brevet-Major. In the winter of 1853-4 he assisted in 
the measurement of the base-line at Attock, the place previously 
selected by the Surveyor-Q«neral as the site for the northern 
base, in company with other chief officers in the Survey. At the 
conclusion of the measurement, the apparatus was transported to 
Kurrachee, the selected site for the southern base operations. 
The principal charge of this second measurement was entrusted 
to Major Strange, under the general superintendence of Colonel 
Waugh, the Surveyor-General, who joined the party at Kurradiee 
on the 6th of December 1854, on which day the measurement 
was commenced, having been finally completed on the 20th of 
the following month. 

On the retirement, in 1855, of Mr. Peyton from the superin- 
tendence of the *' Elastem Coast Series," Major Strange was 
appointed his successor. The surveying work of this " Series " con- 
sist^Hl in carrying a chain of triangles over the eastern coast of 
the Peninsula from Calcutta to Madras, and it proved to be one 
of the most difficult portions of the whole Survey, owing prin- 
cipally to the unhealthy climate, the general unfavourable state 
of the atmosphere, an inaccessible country, and, what probably 
ffavo the most anxiety, an inefficient native staff. The work was 
mquently interrupt<Hi by one or other of the party being laid 
low with jungle fever, which produces a great debility, and 
depression both of the mental and physical powers. In 1857 
Major Strange had a vt^ry severe attack, which compelled him to 
eeok a more bracing climato for the restoration of his health, 
and for a time' he resided at the Neilgherry Hills. On his 
TVOt>voTT, he returned to his duties, and further progress was 
made in the survey ; but on his promotion in i860 to the rank 
of Ro^rimontal Major, and in aciwniance with the usual regnla- 
lions of the Service, he was obligoii to retire from the superin- 
ticindenoe of the Series, and alsi> fn>m the Survey, af^er a connection 
of ihirt^H^n >x^r5 with the IV^virtriiont. Ho was succeeded in 
the char^ of the •' Ka*t or n d^^iVst S^^rit^ " by the late Captain 
Basevi* In iSoi Majinr Stituigt^ ivtumed to England, and 



M. 1877. Fifby^menth Annual General Meeting, 157 

soon afWr retired from the Army with the rank of Lieutenant- 
Colonel. 

The practical experience gained by Colonel Strange during 
Ids yarioiiB snrveying operations, naturally rendered his opinion, 
in connection with the construction of scientific instruments, of 
gnat yalue ; for his proved mechanical skill, and his practical 
bowledge of the use of mathematical, surveying, and astronomic 
cbI instruments, was equalled by few men in this country. In 
1862, the Indian Gk>vemment, desirous of securing the advantages 
of snch a great experience in instrumental matters, entrusted to 
Colonel Strange the task of designing and of superintending the 
coDstraddon of a series of massive and standard instruments, of 
the first order, for the use of the Ghreat Trigonometrical Survey 
of India, and in 1863 he received the appointment of Inspector 
(^ scientific instruments ; his duty to consist of examining and 
testing every instrument purchased in England, and destined 
&r public service in India. For this purpose an observatory 
was erected at the warehouse of the Store Department of the 
India Office, in the Belvedere Road, Lambeth. The class of 
ifistroments usually inspected under Colonel Strange's personal 
laperintendence, consisted principally of those employed in sur- 
veying operations, including telescopes, sextants, theodolites, 
lovelling instruments, barometers, thermometers, and almost 
07617 land of mathematical and drawing instruments. Nearly 
one hundred different kinds have been examined yearly, and in 
iliat time as many as 7,000 instruments, large and small, have 
passed through his hands for service. 

But the principal instrumental work which occupied the 
attention of Colonel Strange, was that required for the com- 
pletion of the large surveying instruments ordered for the Indian 
Snney. These consisted of two zenith-sectors and a great theo- 
dolite, by Troughton and Simms; two five- feet transit instru- 
ments, and two smaller ones, by Cooke ; two twelve-inch vertical 
inmsit instruments, by Repsold ; two galvanic chronographs for 
the registration of transit observations, by Secretan ; and three 
ftfitronomical clocks, by Frodsham. The consideration of the 
best means of construction, of the metal to be employed, the 
preparation of the working drawings, and the preliminary trials 
of the different instruments, absorbed a considerable portion of 
the time devoted by Colonel Strange to his official work. All 
^ was, however, performed without neglecting the general 
ii'spection of the smaller class of instruments. The working 
Swings of the great theodolite were completed as early as May 
1862, embracing the most minute retails in nine large sheets, 
acoompanied by a voluminous specification. 

Colonel Strange joined our Society on the 12th of April 
1861, and he was an active member of our Council, and Foreign 
Secretary, from 1863 to 1873. He was an ardent lover of science 
fi>r its own sake ; and from the date of his return from India, he 
bs been associated in the management of several SocietieSy 



15S Report of the Oouneil to the xxxvn. 4, 

whose objects coincided with his own pecnliar habits of thooght. 
He became a Fellow of the Royal Socieiy on the 2nd of J^ne 
1864, and was a member of the Council from 1867 to 1869. He 
was mnoh interested in the Annual Meetings of the British 
Association, and was a frequent speaker and contributor in 
Section A. He was also connected with the Meteorological 
Society and the Society of Arts. Though Colonel Strange 
was so much occupied with his official work, he had suffi- 
cient leisure to enter heartily into any scheme which had for 
its object the advancement of any branch of science. Most 
of his communications to our Society have a highly practioal 
value, and relate chiefly to improved methods of instrumental 
construction. They exhibit evidence of his great technical 
knowledge of the optician and engineer's workshops, and they 
all add to his reputation as a mechanician of the highest order. 
The following are the titles of his principal papers contained in 
our Memoirs and Monthly Notices : — " On testing the Vertical Axis 
of Altazimuth Instruments ;" " On a Direct Method of Testing 
and Adjusting the Equipoise of Altazimuth Instruments ;" " On 
a Proposed Isolated Flange for Conical Axes ;" " On Aluminium 
Bronze as a Material for the Construction of Astronomical and 
other Philosophical Instruments ;" *' On a Zenith Sector for the 
use of the Trigonometrical Survey of India,*' &c. In his obser- 
vatory at Lambeth, Colonel Strange was frequently occupied in 
purely astronomical work, principally with the object of proving 
the capabilities of his instruments. In consequence of the peculiar, 
and, to some extent, private, nature of the observations, very few 
have been published, although some might have been, tp the ad- 
vantage of astronomy. He was known to have made a careful 
determination of the latitude of his observatory with one of the 
instruments made for the Indian Survey, and the observations, 
if judged by the separate results shown by him to the writer, must 
have been of great excellence. 

Colonel Strange was requested to perform the duties of a 
juror in the International Exhibition of 1862. He undertook 
this important office with much pleasure, as it was one in 
which he could bring his practical knowledge to bear on the 
peculiarities in the construction of the numerous scientifio 
instruments which would come under examination. He served 
also a similar office in the Paris International Exhibition 
of 1867. He had very decided opinions on the question of 
(Jovemmont endowment of scientific research, but though they 
were considered by many as somewhat impracticable, yet very 
few can doubt his own great sincerity in the soundness of the 
views entertained by him on the subject. The appointment by 
her Majesty of the ^* Royal Commission on Scientific Instruction 
and the Advancement of Science," of which the Duke of Devon- 
shire was Chairman, was, in a great measure, the result of his 
persistent advocacy of the necessity for increased Grovemmenfc 
aid for the promotion of scientific research ; and, before his 



Fek 1877. Fi/fy-Mevenih Annual General Meeting. 159 

dnth, be bad the aatisfiiction of knowing that many of his pro- 
poab were adopted hy the Commission, and recommended to the 
GoTemment for their oonaicleration. 

Tiie health of Colonel Strange was not good for several 
monthB before the end came, bnt the announcement of his death 
wiB mieTpeeted, and was received with deep regret by a largo 
aide of scientific friends. He died at the residence of his niece 
inOiiilow Sqnare, London, on the 9th of March 1876, at the 
eomptiative^ early age of fifty-seven. k. d. 



AspRiw Yeates was the second son of Samuel Yeates, a 
wdLknown mathematical and philosophical instrument maker in 
Dublin. He was bom on the 2nd of February 1800. He 
ibowed an early inclination to follow his father's business, and 
kxmg the delivery of a course of lectures in Trinity College, 
I7 Sir Humphrey Davy, both father and son were engaged to 
Most in making the necessary arrangements for the proper illus- 
indons of the lectures. Whilst so employed, young Yeates 
^Tailed himself of the opportunity thus opened to him for im- 
proring his knowledge of the theory and construction of the 
philosophical apparatus used in the experiments. 

When Captain Drummond suggested the idea of applying the 
farilliaiit limelight, which has since been known under his name, 
iot rendering distant stations visible, and which has been found 
10 Talnable in the operations of the Trigonometrical Survey, he 
sppKed to Mr. Samuel Yeates for his aid in the construction of 
tti instrument for showing the limelight to the best advantage. 
Andrew Yeates, to whom was given most of the responsibility of 
^ work, spared no time in making himself acquainted with all 
the details required by Captain Drummond. When he saw the 
gieat brilliancy of the light, and was informed that the chief 
<)hject of the invention was the measurement of distant angles of 
stations made visible by it, though inaccessible, either from being 
■cpftrated by broad channels of water, or from any other cause, 
&nd that the object was the construction of an accurate topo- 
^phical representation of the British Isles, he determined to 
^e himself acquainted with the whole subject, and by perse- 
^onmce and enquiry, he was able to realise the great importance 
^f the operations of the Ordnance Survey, and of the necessity 
^d value of having instruments of precision for that undertak- 
^^- His practical skill in this class of surveying instruments 
^ ftilly acknowledged in his after life. His anxiety to enlarge 
his knowledge of the peculiar details of the instruments used for 
■^^^ejing purposes created a greater desire to become acquainted 
^th the coustroction of larger astronomical instruments, 
^^pecially those at the Royal Observatory at Greenwich, then 
consigting chiefly of Trough ton's Transit and Mural Circle, 
B^sden's Equatoreal, and a few other less noted instruments, 
fie therefore came to England in 1821, and on his arrival in 



i6o Beport of the OawicU to the xnvn. 4« 

London he fortunately made the acquaintance of Tronghton, with 
whom he worked several years. In 1833 he was employed at 
the Observatory, ander the superintendence of the great optician, 
for the readjustment and repair of the instruments — a work which 
he performed not only to the satisfaction of his employer, bat 
also of the Astronomer Royal, Mr. Pond. Having been for a 
long time desirous of becoming acquainted with the details of the 
Greenwich instruments, this work was peculiarly gratifying 
to him. From this time Mr. Yeates applied himseli principally 
to the manufacture of mathematical and surveying instruments, 
in which he has introduced many and important miprovements, 
for which he has received honourable mention on various occa- 
sions. 

Naturally of a studious and retiring disposition, Mr. Yeates 
was little known by the general public, but he was much esteemed 
by a large circle of scientific acquaintances as a careful observer, 
and, as a manufacturer, for the excellency of his instruments. In 
him they could repose confidence in his ability as a mechanician, 
and might rely on his assistance, which he was always ready to 
afford. His health at last failed from a too sedulous appHcation 
to business, from which he eventually retired, and spent hii 
closing years in the enjoyment of a country Ufe, surrounded by 
a select cirde of valued friends. His death took place on 
February 16, 1876, having just completed the seventy-sixth year 
of his age. Mr. Yeates was elected a Fellow of our Society on 
March 8, 1861. He was also a Fellow of the Royal Microscopical 
Society, and a Member of the Socieiy of Arts. 



Feb. 1877. Fifty-seventh Anntial General Meeting. 16 r 



Pboceedings of Obsebvatobies. 

The following Reports of the proceedings of Observatories 
doling the past year have been received by the Council, excepting 
tliat of Melbourne, which has been compiled from Mr. EUery's 
Beport to the Board of Visitors in June last. 



Royal Observatoryy Chreenunch. 

The ordinary observations with the Transit- Circle and Alta- 
BBDiih have been regularly made during the past year, their 
umber being rather larger than usual. For the first three 
BMnihs the readings of the four supplementary microscopes of 
tbTi&Qsit*Circle, as well as of the six ordinary microscopes, which 
Ind been fitted with new micrometer screws, were systematically 
tikea with every observation, and the comparison of the two 
Mis showed that the screws were sensibly free from periodic 
•TOP. To eliminate the effect of wear in future, it is proposed 
to leverse one micrometer in each pair, so that the springs will 
act in opposite directions. It has recently been discovered that 
one of the pivots of the Transit-Circle had been much cut, pro- 
^ly by a grain of sand, which might have accidentally fallen on 
^ Y when the instrument was raised. The roughness has been 
Ciwfully burnished down by Mr. Simms, and a satisfactory 
^nnination of the pivot errors has been made after several 
Mores caused by instability of the apparatus. 

The Sidereal Standard Clock has been cleaned lately, having 
8D0wn considerable irregularities of rate, and finally stopped 
"om the effect of dirt in the train. 

The Great Equatoreal has been almost entirely devoted to 
spectroscopic work, the results of which have, to a great extent, 
**en given in the Monthly Notices. The motions of 34 stars 
"^ve been determined in the past year from the displacement of 
lilies in their spectra, the agreement with Dr. Huggins' results 
being very remarkable, considering the delicacy of the observa- 
"on ; and, as a check on the principle of the method, the dis- 
placement has been measured in the case of the Moon and Vemis, 
for which the motion is known from other considerations. De- 
^^nninations have also been made of the displacement due to the 
notation of the Sun and of Jupiter. No measures have yet been 
<5^ned of the lines in the spectra of nebulas, though a pre- 
liminary examination has been made of several of them. Observa- 
tions have been made of the spectra of Venus, Saturn, and Neptune, 
as Well as of some of the brighter variable stars at maximum 
and minimum, interesting changes having been noted in several 
CMes. No notification of the discovery of the new star in Cygnns 

N 



1 62 Report of the Coufieil to the xxxni. 4, 

on November 24, reached this Observatory till December 9, when 
the star had become faint, and as the Eqaatoreal had then been 
dismantled, it was not fonnd practicable to observe the spectrum 
till the beginning of this year. In connection with the dis- 
placemcDt of the F line in the spectra of stars, measnres of the 
corresponding line of Hydrogen have been made at pressnres 
varying from 4"" to 290"*", which show conclusively that 
the line expands equally on the two sides as the pressure is 
increased, the position of its centre remaining unaltered. At 
the same time, changes have been noted in the relative bright- 
ness of the three principal lines of Hydrogen as the tension 
of the spark and the pressure were varied, the H/3 line alone 
being visible at the pressure of 02°^, which was the lowest at 
which the spectrum was observed. This work was much delayed 
by the necessity for extensive repairs to the Grookes air-pump^ 
and was further hindered by the presence, on many occasions, of 
a complicated spectrum (possibly due to some impurity), which 
overpowered the ordinary spectrum of Hydrogen. The Sun's 
chromosphere has been examined on every favourable oppor- 
tunity, but the prominences have been generally smaU, and on 
30 per cent, of the days of observation were altogether absent. 

In consequence of stiffness in its motion, the Great Equatoreal 
has been examined lately, and the upper pivot has been fonnd to 
have been much worn by the friction-rollers, whilst the pivots of 
the latter had '^ fired." The mischief has been remedied by 
Mr. Simms, who has effected a great improvement in the 
movement of the instrument. The only recent alteration to 
the Spectroscope has been the mounting of the Gollimator- 
object-glass in gymbals, which allow of its being tilted safiB- 
ciently to correct the astigmatism of the prisms. This plan has 
been found to answer perfectly.. 

A Direct-vision Spectroscope has been recently made by 
Mr. Hilger on a now plan, in which advantage is taken of a 
property of the ** Half- prism " to obtain great dispersive power 
with two, or at the most three, " Half- prisms." As this Spectro* 
scope, though on a small scale, appears to be greatly superior 
both in dispersive power and brightness of spectrum to the 
large Spectroscope with its train of ten compound prisma, a 
larger instrument on the same plan is being made by Mr. Hilger 
for the Royal Observatory, and it is anticipated that, inde- 
pendently of its greater power, it will be found to have some 
advantages as regards ease of manipulation over the old form. 

The past year has been very unfavourable for Solar pho- 
tography, only 164 days having been sufficiently clear for this 
purpose, and on 64 of these there was a complete absence of 
spots, though facul89 were usually present. The areas of all spotn 
and faculsB on the photographs have been measured to the end of 
1876, and the determination of their position-angles and dis- 
tances from the centre of the Sun*s disk has been commenced with 
Position-micrometer which Mr. Simms has recently made for 



FeK 1877. Fifty-seventh Annual General Meeting, 163 

the measarement of Solar photographs. With this instmment 
the areas 'will bo determined at the same time as the Helio- 
graphic Co-ordinates. Some photographs of the Moon, Jupiter , 
andetars, as well as of the Solar spectmm, have also been taken. 

The August meteors were successfully observed ; but in 
NoTemher the weather was very unfavourable, and only a few 
meteors were noted on November 14. 

The computations for the Nine-year Catalogue, containing over 
2,250 stars, most of which are observed three or more times in each 
dement, are. considerably advanced, although last year's observa- 
tJons will have to be included in it. The precessions and star- 
constants are all computed in duplicate ; all the observations up to 
the end of 1875 ^^ entered, and about half of them reduced to the 
epoch 1872 ; idl being corrected for inequality in the micrometer 
loiws, which has been a work of some labour. 

The volume for 1874 has been lying for some time past at 
HJL Stationery Office, ready for distribution, but detained there 
utQ the decision of the Treasury is communicated on the ques- 
tion of gratuitous distribution as in past years.* The printing of 
thevolnme for 1875 ^^ ^^^ advanced, the sections of observations 
with the Transit- Circle and Altazimuth being complete ; and the 
redactions for 1876 are in a very forward state, notwithstanding 
the extra work on the Nine-year Catalogue. All the observations 
with the Transit-Circle are completely reduced to the end of the 
year. A detailed report on the progress of the reduction of the 
observations of the Transit of Ventts is given under that head. 



Badcliffe Observatory, Oxford, 

The operations of this Observatory during the past year have 
generally of the same character as in preceding years. 

The volume of the Badcliffe Observations for 1873, of which 
abstract of the contents was given in the last Annual Report 
of this Society, was published and circulated in the spring of 
1«t year. The following volume for 1874 in now ready for dis- 
tribution, and will prol»bly be in the hands of many of the 
FeUows of the Society before the day of the Annual Meeting. Its 
contents are chiefly a catalogue of 1,544 stars, 108 observations 
of the Son, 50 of the Moon, 23 of Mercury, 23 of Venus, 15 of 
J%p4fer, II of Saturn, 10 of Uranus, 6 of Nepiuyie, and 5 of 
CojKgia's Comet, S.P. ; a catalogue of 24 double stars, many of 
which have been repeatedly observed, and 16 measures of the 
disk of Jupiter, giving 3 7"* 16 for the value of the equatoreal 
dxamieter at the unit of distance, and yyV.T ^^^ ^^^ ellipticity. In 
«ldilioxi, there are several series of observations of CoGfgia's 
Comet made with the heliometer, 10 occultations of stars by 
the Moon, thoroughly reduced, and 39 observations of phenomena 

• See Foot Note on page 143. 

N 2 



1^4 Report oj the Council to the XXXTII. 4, 

of Jupiter* 8 satellites ; and, finally, a considerable number of ob- 
servations of shooting stars. The meteorological portion of the 
volume contains the usual quantity of matter, carefully arranged, 
and the same labour has been bestowed on the reduction of the 
observations as heretofore. 

The reduction of the astronomical observations for 1875 
has been essentially completed for some time, and the printing 
of the volume has commenced, three half-sheets of the Rigkl 
Ascensions of stars having been printed. 

The weather during considerable portions of the year 1876 
was, as is well-known, very cloudy, and the amount of observaticmf 
may therefore not be quite so great as in preceding years, though 
it does not fall very far short of it. The reductions for this jefm 
(1876) are in a forward state. 

But probably the work which will be looked on with Um 
greatest interest by astronomers generally is the compilation of a 
Tliird Radcliffe Catalogue of Stars, which has been begun daring 
the past year, and in which considerable progress has been made. 
An iudex-oatalogne has been formed of all the stars, arranged in 
order of their Right Ascensions, contained in the volumes com* 
mencing with 1862 and ending with 1870, which are the limits 
decided on for the catalogue, and it is found that the total 
number of distinct stars in this interval is nearly 4,400. 

Of these, all the results, both for R.A. and N.P.D., have been 
written out in sheets prepared and printed for the purpose as fiu 
as the end of the tenth hour of Right Ascension, and this workti 
being rapidly carried forward by Mr. Luff, who has charge of thi 
compilation of the catalogue. 

As there is no extra assistance, the completion of the worl 
cannot, of course, be looked for very early ; but it is hoped thai 
the ordinary staff of the Observatory will suffice to prevent an] 
suspension of it for other purposes, and that it will go steadily, i 
not rapidly, on towards completion. 

The reduction of the meteorological observations is, witl 
regard to arrears, in the usual state, and it does not seem possibV 
to advance it much, though no practical inconvenience witl 
respect to the printing is experienced by this circumstance. 



Oxford University Observatory. 

This Observatory has now been in active operation for littl 
more than a year, and the first report of its proceedings has beei 
published and presented to the Convocation of the University. Thi 
latter body has, with great but not unusual generosity, increase! 
the pecuniary grant for the maintenance of the establishment. 

Three hundred and fifty photographs of the Moon have beei 
taken with the De La Rue Reflector during the year, and the^ 



Feb. 1877. Fifly-seventh Annual General Meeting. 165 

are still rapidly accninnlating. The time is approaching when 
these autograpnic registers are to be utilised for the determina- 
tion of the natation, or inequality of the libration, of the Moon's 
axis. The att<ention of Professor Pritchard is now directed to 
the preparation of the details of the necessary mathematical 
processes; and Mr. De La Rue has undertaken to devise and 
provide a micrometer suitable for the measurements of these 
hinar photographs. Concurrently with these preparations the 
Professor proposes to set on foot a series of measurements with the 
lirge Refracting Telescope of five well marked and suitable points 
oithe Moon's disk, so as to provide a check or a verification of 
the photographic measures. A few photographs have been taken 
of certain double stars, and of Venus and Jupiter, at present 
■•mlj to gain experience. 

The satellites of Saturn have been observed during thirty- 
tvo nights. The results have been reduced, and, together with 
• former similar series, will very soon be in a condition for 
pvhlication. 

Two hundred double stars have been measured during the 
y^; these observations also are in a state i*cady ior printing. 
Considerable time and labour have been bestowed on the calcula- 
tion of the orbits of certain binary stars, which hold out the 
^'pectation of definite results. In common with other astro- 
iwmers, we have greatly deplored the want of sufficiently 
JMunepous and accordant observations. The method adopted 
n» this Observatory for the determination of these orbits 
tt a combination of both the graphical and the computa- 
**^1 determination of the elements; and it is believed that 
considerable advantages have been thereby secured. In the 
c'^'Be of these calculations a new and very simple mechanical 
Jl^thod of calculating the excentric anomaly has occurred to 
j^essor Pritchard, and thereby much tedious arithmetic has 
**^ avoided. It saves all the preliminary trials in the tentative 
'^ods for the exact calculation of the excentric anomaly. 

T'he beautiful Sun Spectroscope devised by Mr. Grubb has 
^ nearly ruined by a certain violent maltreatment which it 
J*twith in its transit along the railway to Dublin, whither it 
J*fl been sent for a slight but necessary modification. Its return 
^Oxford is shortly expected, when restored at the expense of 
"* railway authorities. The large Equatoreal continues to give 
^^ entire satisfaction. 

Before closing this report it may not be altogether unin- 
^''ftjting to the Society to remind them that, concurrently with 
^^ prosecution of original research, one important object which 
If^nted itself to the University of Oxford in the institution of 
^ establishment was the resuscitation of the science of astro- 
•^y among the students in this ancient seat of learning. The 
P^t increase of the numbers who now attend the Professor's 
*cture8 in the Observatory affords the prospect of the realisa- 
^ of this hope. In furtherance of the same object the 



1 66 Report of the Council to the xxxvii. 4, 

Convocation of the University Lave recently authorised the Vioe- 
Chancellor to beek the advice of Mr. Charles Barry in the erectiov 
of a suitable lecture room and library for the use of RtadentB 
These additions have, in fact, become an absolute necessity foi 
the success of the institution, so far as University studies an 
concerned. 

It has been asked more than once, and by none so anzioiiflL 
as by the late illustrious Wilhelm Struve, when he was a Pic 
f essor at Dorpat, whether the co-existence of instruction is detr- 
mental or otherwise to the business and the original work rv 
quired in an Astronomical Observatory. Professor PritoharA 
experience is, that so long as it is kept within its due limits, ^ 
devotion of a portion of the Director's attention, during a past <M 
the year, to the instruction of the highest and most intelligent 
order of students in a great University like that of Oxford is not 
only of great advantage to the studies of the place, bat in 
many respects it is beneficial to the Professor himself. It pro- 
vides the astronomer with fresh interests and a pleasant vanely 
of occupation, while it necessitates increased precision and 
methodical arrangement in his own mind. Further than that 
the eager and ingenious cnriosity of fresh and cultivated intd 
lects will not seldom set the Professor on the path of net 
enquiries, or stimulate him to the removal of old obscurities. 



Camhridye Ohseivatory. 

In a year exceptionally unfavourable for astronomical obsei 
vations, the places of 3,455 small stars have been obtained, a 
well as observations of the standard stars required for clock an 
instrumental corrections. 

Since the mounting of the Transit- Circle, the inclination • 
the axis to the horizon has been gradually increasing, until 
amounted to nearly seven seconds, the east end being the highe 
Mr. Simms has lately reduced the support of the eastern pivt 
by scraping, so as to make the axis more nearly level. The we 
end is now higher by rather more than one second. 

In order to improve the illumination of the wires in a dai 
field, Mr. Simms has given a cylindrical form to one surface 
the prisms in the eye-piece. Although some improvement 
thus effected, the light is not yet sufficient for satisfactory obae 
vation. This is of the less consequence, however, as it is foni 
that by placing a coloured glass before the perforation in € 
axis, the light in the field can be moderated, so that stars may 1 
observed in the ordinary way to the lowest limit requii*ed in tl 
Zone observations. 

The discrepancy in the Nadir- point of the Transit- Gild 
arising from shake in the telescope tube, had been ali^ac 



Feb. 1877. Fifty^seventh Annual Oeneral Meeting, 167 

reduced to a very small quantity, not exceeding abont one-tenth 
uf its original amount, by means of screws connecting the outer 
and inner portions of the tube. Mr. Simms has now inserted 
sponger screws than before, and it is hoped that, in consequence, 
this discrepancy will entirely disappear. 

The alterations kept the Transit- Circle idle during November 
and December, but this is the less to be regretted, as there was 
hardly a night on which Zone stars could have been observed. 

By means of some additional assistance in computation, 
applied by the Sheepshanks Fund, satisfactory progress is being 
Dade with the reductions. 

All the observations are entered in the reduction books, and 
this means taken. 

The reductions of standard stars, both in Bight Ascension 
ad North Polar distance, are completed to the end of 1875, 
ad the Bight Ascensions for 1876 are approaching completion. 

The apparent North Polar distances of the Zone stars are 
ohtained as far as the end of 1873, and the calculation of the 
Bight Ascension is now in progress. 

The Transit Clock was taken to London in March 1876, by 
Mr. James Brock, of 64 George Street, and underwent a thorougn 
examination and cleaning. Since that time its rate has been 
much more satisfactory than before. 

A new line of railway in connection with the Great Northern 
system has been lately projected, which is to pass at the distance 
of about 550 yards from the Observatory, between it and the 
^wn of Cambridge. It is hoped that this scheme will not be 
<5*>Tied out, as it is Professor Adams's opinion that so great a 
proximity of the line would be very injurious to the work of the 
Observatory. 



Dunsink Observatory, 

During the year the Meridian- Circle has been employed in 
^tmuing the observations of the Bed Stars contained in Dr. 
SchjeUerup's catalogue. Other stars have been from time to time 
•dded to the working list, chiefly taken from the extensive cata- 
^<%ue of Bed Stars, prepared by Mr. Birmingham, and now in 
pODrse of publication. The reductions of these observations are 
^ progress, and have advanced considerably since the date of 
*fe last Beport. It is intended that each of the stars referred 
*o shall have its co-ordinates determined at least twice in each of 
^ positions of the instrument. Several of the minor planets 
We been observed as opportunity offered during the year, and 
their places are now being compared with those of the Ephe- 
Oierides of the Berliner JaJirhuch. 

In October 1876, a series of observations of Polaris was 



1 68 Report of tJie Cotmcil to tlt^ XXXYII. 4, 

commenced for the improyement of the adopted co-latitude, and 
has been continued to the present date. During each set of 
observations of Polaris, above or below the pole, the Transit- 
Circle is twice reversed, and the observations are equally divided 
between tbe two positions of the instrument. Half the obeerva- 
tions are direct, and half by reflexion, distributed as sym- 
metrically as is practicable. It is contemplated to continue this 
series for some time to come. 

The South Equatoreal is being employed in the investigation 
of the parallaxes of some of the Red Stars above mentioned, 
together with other stars of physical interest, either on aoconni 
of variable light, large proper motion, or unusual spectra. A 
great number of measures have been made, and their reductioi] 
IS being actively proceeded with. 

In addition to the new Sidereal Clock, by E. Dent & Go. 
mentioned in last year's Keport, and used up to the present time 
the Observatory now possesses an excellent Mean Time Standard 
Clock, by Booth, of Dublin, which is employed for the electric 
control of a clock at the office of the Dublin Port and Docks 
Board. 

A Chronograph, with two barrels, for registration of obseT' 
vations made with the Transit-Circle and South Equatoreal, hac 
been ordered from Mr. Grubb. 



The lioijal Observatory, Edinburgh. 

The Budget granted by H.M. Government for the support o 
the Royal Observatory, Edinburgh, during the past year, for aJ 
salaries and all office expenses therein, has been nnder :^i,ioo. 

The work performed at the same time by the Astronomer am 
the two assistant astronomers thence maintained, has been : — 

1 . The service of daily distributing correct time by means 
electric time-ball, time-gun, and controlled clocks. 

2. The computation of the meteorological observations take: 
twice a day throughout the year at 55 stations of the Scottia 
Meteorological Society, for the Registrar- General in Scotland. 

3. Calculations for the Edinburgh Star Catalogue; at whic 
the Astronomer reports that the two assistant astronomers. Mi 
Alexander Wallace, M.A., and Mr. Thomas Heath, B.A., hav 
greatly distinguished themselves for steady and untiring devc 
tion, both by day and by night, to the multitudinous figni 
work required. 

Among the chief incidents during the period have been :— 

1. In January 1876, the temporary contribution by the Astn 
nomer of several pieces of apparatus to the Loan Collection < 
Scientific Instruments at South Kensington, London. 

2. In February, the appointment by H. M. Office of Works i 



Feb. 1877. Fifty'Seventk Annual Qeneral Meeting. 169 

London, of Mr. Christie, of Greenwich, to examine the Edinbmgh 
Eqoatoreal, not yet oat of their contract with the maker, and to 
report to them npon it. 

3. In Jane, tiie construction in France, at the Astronomer's 
priTate expense, of a large spectroscopic instrument, snch as the 
Royal Observatory, Edinburgh, has long been in argent need of, 
bat was never able to obtain the necessary funds for, from any 
other quarter. 

4. In July, the arrival of a Government Conmiission of En- 
qoirj, under the presidency of Lord Lindsay, to report upon 
eTerything relating to the Observatory. 

5. In September, the breakage, by a mad sailor from Leith, 
of the whole of the Observatory's deep- soil thermometers, whose 
ngolar observation, during 39 years past, has formed a distinct 
ttd not unimportant branch of the work of the Observatory. 
Ae man who conmiitted the mischief is now in a lunatic 
Mylnm maintained at the public expense ; but the Observatory 
ta no funds wherewith to repair its dismal loss. 

6. In December 1876, the furnishing by the Astronomer, 
at command of H.M. Principal Secretary of State for Home 
'^ffiurs, the Bight Hon. B. Assheton Cross, M.P., suggestions as 
^ renewing the deep-soil thermometers ; these being viewed as 
'^'^tniments successftdly proved by previous experience here, and 
JopB recently at the Boyal Observatory, Greenwich, to have a 
«JiBct bearing on certain grand cycles of other than annual heat- 
^^ee affecting the Earth from without. 



Glasgow Observatory. 

The operations at the Glasgow Observatory during the past 

JJ^^T have mainly consisted in reducing to the mean equinox 

^ ^ 870, and preparing for the press, the meridional observations 

. stars, which have been accumulating at the Observatory 

"^^fie the year i860. The task is a very laborious one, as is 

JT^ll known to those who have had experience of such observa- 

^tis; but in an Observatory like that of Glasgow, where the 

P^t>vision for assistance is on a very limited scale, it is especiaUy 

!^- Professor Grant has recently called the attention of the Town 

Jr^nncil of Glasgow and the Clyde Trustees to the desirability of 

r*^r co-operating with the Observatory more effectually than 

*^^retofore in supplying the City and Port of Glasgow with the 

^vantages of correct time. The Town Council have cordially 

*^en up the subject, and it is probable that ere long a con- 

^derablo extension will be given to the system of controlling 

clocks by electricity, which has been in successful operation 

We during the last thirteen years. 



, 170 Beport of the Council to ths XXXYIL 4, 

Kew Observatory, 

The photoheliograph not being in use at Kew has been 
deposited for the past year in the Loan Collection at South 
Kensington, where it has been exhibited, together with a number 
of Solar negatives. 

The re-examination of the measurements of the Kew Son 
pictures, taken daring the ten yeai's 1 862-1 871, has been steadily 
carried on under Mr. De La Rue's direction, and has now advanced 
as far as the middle of 1870. Progress is somewhat slow at 
present, owing to the enormous number of spots which the 
pictures contain at this epoch, many of them having over forty, 
of which accurate determinations of position are made. A correc- 
tion for the optical distortion of every picture is now being 
applied to the measurements. 

The ephemerides for the whole period of the Kew Sun-spot 
observations have been re-calculated by Mr. Marth, and are now 
in the Observatory. Mr. Marth is now engaged on the reduc- 
tion of the measurements of the Solar photograms. 

At the request of Mr. Hind to Mr. De La Rue, a careful inspec- 
tion has been made of the Kew Sun pictures from 1858 to 1875, 
with a view to obtain evidence as to the existence of the iutjra- 
Mercurial planet. The observations bearing on the question 
have been communicated to that gentleman. The whole of th^ 
expense attendant on the Sun work has been borne by Mr. De Lfl 
Bue. 

Mr. C. S. Peirce, of the United States Coast Survey, who 
has recently been making pendulum observations at Berlin^ 
Geneva, and Paris, arrived at the Observatory in June; afbei 
having had the necessary fittings put up in the pendulum-room, 
he erected his apparatus, and made a complete series of vibra< 
tions. He has since returned to America. 

The magnetical and meteorological work, to which the atten- 
tion of the Observatory is chiefly directed, has been prosecutec 
continuously, and a large number of instruments have under- 
gone verification in the department devoted to that duty. 



Liverpool Observatory, Bidston, Birkenhead. 

No important change has been made in the working of thi 
Observatory during the past year. 

About 300 new chronometers are tested annually in the thre* 
definite temperatures of 55°, 70°, and 85° of Fahrenheit. 

Makers are much more successful than formerly in so adjust 
ing the weights on the balance, that the maximum gaining rat 
shall bo at about 70° of Fahrenheit. 



Peb. 1877. Ftfty-sevevih Anntuil Qeneral Meeting, 171 

The averBge loss at 15° from the temperature of maximum 
gaining rate is still fonnd to be between six and seven tenths 
of a second, and at 30^ between two and three seconds a day. 

About twenty years ago, a few chronometers were tested at 
the old Liverpool Observatory, the balance rims of which were 
cat throagh at 90° from each end of the balance arm, and 
four small weights were used. By means of three holes, for 
small screws, between each weight and the balance arm, the 
final adjustments for compensation were greatly ^cilitated. The 
I0B8 at 30^ from the temperature of maximum gaining rate, in 
cbionometers with balances so made, did not appear to be more 
than the loss at 15^ with balances made in the ordinary way. 
This subject is well worthy the attention of chronometer 
miners. 



Temple Observatory^ Bnujhy. 

The measurement of the positions and distances of double 
stars has, as in previous years, been the chief work of this 
Observatory. Owing principally to the unusually bad weather, 
the nnmber of stars measured, 183, is somewhat small. The 
selection includes many stars of which the binary character is 
more or less doubtful, the examination of which has been under- 
taken in preparation for the list of double stars recently pre- 
sented to the Society by Mr. Wilson and Mr. Gledhill. 

The spectroscopic observations of the Sun have been dis- 
continued, as they are now regularly made at places which enjoy 
a better climate. The earlier observations have been published 
"7 the Royal Society in conjunction with Mr. Lockyer's ; and 
those of later years will be published by the Rugby Natural 
History Society. 

The Spectroscope on the 12-inch reflector has been arrangred 
hy Mr. Seabroke, for the examination of the spectra of stars, 
^th the view to obtain confirmatory measures of the rates of 
their approach or recession, and some progress has been made in 
this direction. 

As in previous years, considerable attention has been paid to 
the educational use of the Observatory, which receives many 
visits from members of the school. 

The existing wooden Observatory being in a bad state of 
^pair, it has been decided to build a new and permanent one, 
^th a curator's cottage adjoining, and the Governing Body have 
Purchased a suitable site. They are, however, unable to con- 
tnbute towards the expense of building; and a fund is being 
accumulated for this purpose. Mr. E. Crossley has presented 
a tianait instrument, and Mr. Wilson would most thankfully 
^^ive any gifts, whether of money, instruments, books, or 



172 Report of the Gomicil to the niXYlL At 

photographs, which will advance the ohjects of the Observatory, 
The sabBcriptions at present amount to about JC425, and the 
total sum required will not be less than £1,000. 



Stonyhurst Observatory, 

The astronomical work at this Observatory during the past 
year has been somewhat interfered with by the sickness of the 
first assistant, and by the change of the computer in the meteoro- 
logical department. The uninterrupted series of meteorological 
and magnetic observations, and their reduction, demanded most 
of our time, but the phenomena of Jupiter* s satellites, and the 
usual watch for meteors, were not neglected. A number of ex- 
periments wore made with the spectroscope for determining the 
easiest method for simultaneous observation of the chromosphere 
and solar limb, with the view of preparing for the Transit of 
Ventis in 1882, or any similar phenomenon. Previous to this year 
the Observatory was not provided with a chronograph, but one 
has lately been procured from Paris, to be used principaUy for 
small differences of B.A., in mapping small portions of the 
heavens, and in observations of Mara this year. More time than 
usual has been devoted lately to the instruction of students in 
methods of observation. 



Mr. Barclay*8 Observatory, Leyton, Essex, 

The work of the past year has mainly been the observations 
of double stars. Eclipses, occultations, and phenomena of 
Jxiptter*$ satellites have also been observed when possible. It is 
proiK>seil to publish a fourth volume of Observations at the close 
of the present year. 

For the last two years the weather here has not been very 
£ftvourable for astronomical work. 



Ifr. Bishop* s Observatory^ Txrickenham. 

Mr. Bishop's Ol>8er\-atory was closoii at the end of last year. 
Purposing to reside for the fixator part of the year in the 
Simth of Kun.>pe, it has Ixvu his intention for some time past to 
relint^ui:^ astronomical observations at Twickenham, and during 
the last filteen mouths the Observatory has only been retained 
in o[>eration with the view to endeavour to complete several of 
the charts of small stars lying near the ecliptic, chiefly where it 



"Feb. 1877. Fiftij'seventh Annual Oeneral Meeting. 173 

Vb crossed by the Via Lactea, and conBcqnently where the formation 
of sach charts, firom the great number of the stars, is necessarily 
very slow and tedious. The weather of the past twelve months 
bas been generally unfavourable for such work in this locality, 
bat two additional charts have been completed. Variable stars, 
prmcipally those detected at Twickenham, have been watched 
on nights when the small star- work could not bo advantageously 
proceeded with, and a list of these stars, with particulars show- 
ing the grounds upon which their variability has been inferred, 
is ready for the press, and will shortly be distributed, together 
with the original observations of comets, ».e. differences of B.A. 
and declination with comparison stars, taken at the Observa- 
tory. 

Mr. Bishop has presented his 7-inch equatoreally-mounted 
refractor, and other instruments, with his astronomical library, 
to the Boyal Observatory at Naples, to which they are now in 
coarse of remoyal. 



Colonel Cooper*8 Observatory^ Marhree. 

MicTometrical measures of double stars have been continued 
by Dr. Doberck during the past year. The usual meteorological 
observations in the manner described in the previous Report have 
also been made. The exposure of the refractor in the open air 
for 80 many years, without proper protection from wind and rain, 
has seriously affected the instrument, which Dr. Doberck fears 
can never be remedied. 



Mr. Edward Crossleifs Observatory^ Bemierside, Halifax. 

As in previous years, the observer's attention has been 
directed almost exclusively to the measurement of double stars. 
The well-known binaries have been measured as often as the 
exceedingly bad observing weather permitted, and a large number 
of 2's stars have been examined with a view to the formation 
01 a complete list of those deserving of careful attention for some 
years to come. 

The weather of 1876 was very bad. The number of nights 
^ which some work could be done was 75 ; of these 40 were bad 
*nd 34 fair: one only was fine enough throughout for the 
^^leaanrement of the most difficult objects. 

Very complete lists of measures of all the most interesting 
Qouble stars have been collected, and much historical matter 
gleaned from the scientific journals, transactions, <fcc., which are 
^ be found in the Society's library. 



174 Report of the Council to ih^. xixyn* 4, 



Mr, Rugging^ Observatory. 

Dnring the last two years arrangements have been in pfD- 
gress for the application of photography to the spectra of the 
stars. For this pnrpose a Reflector with a speculum of r8 inche8 
diameter has been mounted in the place of the 1 5-inch Befractor. 
The motion of the driving clock was then found to be not 
sufficiently uniform for these observations. Mr. Grubb, hj 
means of an original contrivance, has successfully applied to the 
clock the control of a seconds pendulum in electric connection 
with a sidereal clock. This system works quite satisfactorily. 

The spectroscopic part of the apparatus is constructed with 
a prism of Iceland spar and lenses of quartz. Tbis apparatus 
is so arranged that a solar or electric spectrum can be Ix^ken on 
the same plate, for comparison with the spectrum of the star. 

After an extensive trial of different photographic processes, 
preference has been given to dry plates. Among other advan- 
tages, a dry plate can be left in the apparatus until the following 
day, when a solar spectrum can be taken upon it through the 
half of the slit which was closed when the instrument was 
directed to the star. 

In the early part of 1863 photographs of the spectrum of 
Sirttts were taken in this Observatory, but from several causes no 
distinct indications of lines were obtained. Other investigationB 
prevented these experiments from being pursued furtber at 
that time, but the intention of continuing them was never 
abandoned. 

During the past year spectra with distinct lines of Sin'uB^ 
TV(7rt, Vt*tnts^ and the Moon, have been obtained in juxtaposition 
with well-defined and detailed solar spectra. The continuously 
unfavourable weather for the last few months has prevented 
as* yet the extension of this investigation to the spectra of other 
stars. 



TsOi^I Liiuhay^s Ohsenuitory, Dun Echt, Aberdeen. 

The ivftst year has Won chiefly devoted to the continuation of 
the roiluotion of observations immediately connected witb the 
Transit of IV»m*. At the same time, many of the instruments 
used at Mauritius have Invn n^mounteil and tested. 

The 15-ineh (Irubb ri^fraotor has Invn revised in several of its 
details, and a few olv^ervations have htvn taken with it. In par- 
ticular may Ik» mentioniHl determinations of the wave-lengtbs of 
the bright lines in the s^HH^tnun of Dr. Si*hmidt's Xov*, 



E^ieb. 1877. Ftfiy'SevetUh Annual O&neral Meeting, 175 



The Earl of Rosse's Ohservcdory, Birr Castle, Parsonstovm. 

The past year has been about an average one for astronomical 
ork at Parsonstowu. 

On 41 nights 161 sets for nebulae have been made with the 
G-foot reflector, and eight observations with the 3-foot are 
recorded. 

The satellites of Saturn were observed on fonr and that of 
Neptune on two nights. 

The work with the 6-foot consists chiefly of micro- 
metrical measores, and has been directed as far as possible to 
points on which, in preparing past observations for publication, 
briber examination seemed most required. 

The 3-foot is now re-mounted as an equatoreal in, it is believed, 
I Toy satisfactory manner. It remains of the Newtonian form, 
bat it is intended to arrange for its occssional employment in the 
flandielian, or front view form, and this has been all along kept 
n yief^. The instrument has been found extremely steady, and 
I<ord Rosse's assistant, who has observed with it on windy nights, 
h>8 never complained of the least vibration. The clock appears 
to carry it with sufficient regularity for ordinary work in Right 
Asoension without the assistance of the controlling pendulum, 
which was ready for application. The gallery and telescope can 
^ moved with ease, and the motions of both within a considerable 
'^Qge are within the control of the observer. When arrangements 
We been made for enabling him to read the setting circles from 
the eye-piece, and a collimator for correcting the axis of collimation 
W been fitted, Lord Rosse believes that he shall possess an 
instrument from which, owing to its universality of range and its 
general handiness, much useful work may be expected, notwith- 
standing its inferiority to the 6-foot in " space penetrating power." 

It is intended after a few small additions (including those 
'^ntioned above) have been satisfactorily carried out, to describe 
"j% the mounting, which differs in several particulars from any 
hitherto constructed, and of which a model, showing the general 
'''^iijfement, has been deposited in the Loan Exhibition of 
Scientific Instruments. 

The meteorological observations continue to be made without 
*'^ration, and a monthly return is sent to the Meteorological 
^ffice. The return of rainfall for the year only is sent to 
"f. Symons, and the Observatory has been just selected as one 
of fonr which are to send weekly returns of temperature to the 
^gistrar- General for Ireland. 



Colcnid Tomllne*n Ohse^'vafory, Orwell Park, Ipsimch, 

Observations were made at this Observatory during the sprin^r 
of lant year for the comparison of the light of Venus with that of 



176 Report of the Council to the xxxyir. 4, 

the fall Moon, and afler soveral attempts a most snccossiiil result 
lias been obtained, which has already been communicated to the 
Society. The equatoreal has been employed to make a aeries 
of comparisons of Vemis with \ Oeminonim near the time d 
their conjunction on August 17 last, and, although only with 
partial success, some &cts were elicited that have been' thought 
of sufficient interest to merit the notice of astronomers. 

With the meridian instrument it has been found possible to 
complete the determination of the longitude of the Observatory 
from transits of the Moon and culminators. 

A comparison of the Bight Ascensions of the catalogues of 
Greenwich (1864) and Armagh, has shown that, of 2,028 Btam 
whoso proper motions have been investigated, 196, or nearly 
10 per cent., differ by a larger amount from the present adopted 
proper motions than can be supposed to be due to errors in the 
catalogue places themselves. Each of these stars has therefore 
been observed upon the meridian on three separate occasions, in 
order to obtain the latest possible data for the fxirther prosecution 
of the enquiry. The reduction of these observations, together 
with those for the determination of the longitude, are now being 
proceeded with. 

Owing to the non-discovery of comets during the last two 
years, the main feature in the plan of operations proposed for the 
work of this Observatory cannot as yet be carried out. Among 
the questions that may enter into the plans for the ensuing year 
it is hoped that stellar photometry may take a prominent place. 



Royal Observatory y Gape of Good Hope. 

The volume containing the Meridian Observations made 
during the years 1871, 1872, and 1873 has boon distributed for 
the use of astronomers. It contains positions of all the stars in 
Lacaille's zones, and some other stars of about the seventh mag- 
nitude, within fifteen degrees of the South Pole. 

A printed copy of the volume of Results, 1874, but without 
the Introduction, which is not yet passed through the press, is 
forwarded with the present report. 

The Catalogue for 1874 contains the mean places of 1,246 
stars; nearly all observed three times. The stars consist chiefly 
of Lacaillo- stars, in the zone 165° to 155° N.P.D. The dis- 
cordance between the Nadir points which existed in 1871 to 1873 
has sensibly disappeared, since the readjustment of the Transit- 
Circle by Mr. Stone. The corrected results of 1871-1873 ag^e, 
however, very closely with the corresponding observations made 
in 1874. 

A Catalogue has been formed from the observations made 
here from 1834 to 1840, both inclusive. Some considerable 



eb. 1377. Fifiif'Sevenih Annual General Meeting. 177 

no^resB has been made in the printing, but this has been stopped 
or some time, to allow of the results for 1874 being passed 
ihro^ogh the press. 

n7be observations made during the year 1875 are reduced to 
DfiSkxi places. The Catalogue will contain positions of more than 
2,000 stars, chiefly from Lacaille's zones, 155^ to 145° N.P.D. 
Eacli. star has been usually observed three times. 

The observations made in 1876 have consisted chiefly of 

I^caille stars in the zone 145^ to 135^ N.P.D., but many stars of 

ibe serenth magnitude, not in LacaUle, have also been observed. 

The total number of sters observed is about 2,200, and, with the 

exception of 10 or 12 which have only been observed twice, esch 

iter has been observed three times. 

The working Catalogue for 1877 contains Lacaille stars in the 
UM 135° to 125° N.P.D., Brisbane's stars of not less than the 
Kinth magnitude which have not yet been observed, and a few 
■tmi of the eastern zones which it has appeared desirable to 
n-obserre. 

Arrangements have been made for the formation of a general 
<!>tiIogiie, which is intended to include all the observations made 
l>^firom 1871 to 1878. Some considerable progress has been 
Bttde in the systematic preparation of the materials already 
coDected, but much more might be done in that direction if our 
computing staff* were slightly increased. 

The Photoheliograph was mounted and brought regularly 
into nae in February 1876. Photographs were obtained on every 
dear day during the months of February, March, and April, but 
^ Weather then broke up, and it has been found impossible to 
^'ny on the work with reiralarity without an increase of the 
tiff, or without serioHBlj inten-Dptbg the works in progress. 
This has not been considered desirable. The photographs were 
J^taken by Mr. Stone without assistance. A considerable num- 
^ of absolute determinations of the magnetic elements have 
**^ taken by Mr. Stone during the year 1876. 

The Meteorological observations have been taken with regu- 
*"t^y, and reduced. 

A distribution of time over a considerable portion of the 
Colony has been carried out with accuracy and a legularity only 
hmited by occasional breaks in the telegraphic communications. 
The work of the year has to some extent been interrupted 
r^.the resignation of one of the assistants, and a long delay in 
fiiling up the appointment. 



Melhmime Observatory, 

It appears from Mr. Ellery's last Report to the Board of 
' witoTs of the Melbourne Observatory that the general work of 
^ preceding year has been carried on in the same manner as 
kfore, the observations with the TranRit-Circle being limited as 

o 



178 Bepcrt of the Oowncil to the xxxvn. 4, 

much as possible, so as to allow more time for the compilation of 
the animal catalogues, which were in considerable arrear. The 
subjects of observation during the year were the usual standard 
stars for clock-error, the stars used for the determination of 
azimuthal error, and a series of special stars observed by the 
American Transit of Venus party in New Zealand for finding th» 
latitude of their station. The number of stars observed in Righb 
Ascension was 1,211, and in polar distance 454. 

The great telescope has been employed regularly for the 
examination of the nebnlsB and clusters previously delineated by 
Sir John Herschel. Seventy of these have been examined, 
measured, and sketched ; most of them are carefully drawn and 
described, and are ready for publication. Mr. Ellery remarks 
that the drawings and measurements indicate that several of the 
nebulae are cocsiderably changed, while others appear so com- 
pletely altered as to be scarcely recognisable, except by their 
relative position to the neighbouring stars. AH these changes 
have been carefully noted. During the year there were 150 
nights more or less fit for observing with the great telescope, but 
of these forty were solely occupied with visitors, and quite lost 
for astronomical work. Perhaps, as an act of policy, this great 
interference in the observing duties of the staff may be necessary 
in a Colonial Observatory, but it seems rather too great a sacrifice 
to give up more than a quarter of the stated work of the observers 
to satisfy the curiosity of unprofessional st-ar-gazers. 

Several drawings of Mars and Jupiter have been made— of the 
former in June 1875, and of the latter in May 1876. Observations 
also of the conjunction of Saturn* s satellites were made in 1875, 
from August 26 to December 29, with the view of more accurately 
determining their periods. Ten only out of ninety conjunctions 
could be observed, owing to so much cloudy weather. These 
observations were intended to be continued in the autumn of 1876. 

The photohcliograph has been employed, and a Sun picture 
has been obtained on almost every day that the sky was suffi- 
ciently clear. During the year 143 heliograms have been secured* 

In the regular work of the Observatory for the ensuing year 
Mr. Ellery intends to continue the observations with the Transit- 
Circle, as the fundamental work of the establishment. The revision 
of Sir John Herschel's figured nebulse is to be continued with the 
great telescope, and the same instrument will also be employed 
upon occasional planetary observations. In connection with this 
telescope, Mr. Ellery remarks : — " I may mention that, althongb 
the mirrors retain their high reflecting polish exceedingly well, 
the fact must not be overlooked that the time when they will have 
to be repolished will inevitably arrive, and that perhaps earlier 
than we now anticipate. I intend, therefore, to devote some time 
this year to practice in grinding and polishing large surfaces, in 
order that both Mr. Turner and myself may obtain f uiiiher expe- 
rience in the matter. I also hope to personally undertake a 
serieB of observations with the south equatorcal (8-inch), more 



Feb. 1877* lyty-ievenih Annual Gkneral Meeting , tjg 

especiallj of the objects to be observed with the great telescope, 
for the purpose of micrometric measurements, which will, I anti- 
dpate, enable the larger instrument to be devoted more excln- 
nrelj to the figoring and revision of the featnres of the nebnlaa." 
During his recent visit to Europe, Mr. Ellerj made enquiries 
concerning the best means of reproducing for publication the valu- 
able collection of drawings of nebulaB now in hand ; but though he 
ingpected manj proposed methods, the result was not satis&ctorv. 
He has since seen, however, some specimens of a toned lithograpn, 
white on black ground, the work of an officer attached to the 
Mining Department, on which the nebulsB are represented as they 
appear in the telescope more nearly than by any other method 
which he has examined. There is, therefore, some hope that the 
nanlts of the observations of the Great Melbourne Telescope will, 
ai BO distant date, be in the hands of astronomers, as ijiere is 
ihttdj a considerable amount of work of ^reat interest ready 
fcr publication as soon as the method to be employed in the 
nproduction of the nebnlca is decided on. 



2 



l8o Meport of the Oounbil to ilie xtXYVL, 4, 



Notes on some Points connected with the Progress or 
Astronomy dukiKg the Past Year. 



TJie Numerical Lvmar TJieory. 

The Namerical Lanar Theory, on the state of which the 
Astronomer-Rojal has occasionally given some Reports to the 
Society, has advanced steadily, interrapted only by some errors 
in operations incurred by an assistant's trusting too mnch to his 
own mdgment and accuracy. With the view of placing the work 
which is done in a position of safety against ordinary oon* 
tingenoies, a considerable portion has been already printed, in 
readiness for ultimate distribution, both as an Appendix to the 
Greenwich Observations and as an independent treatise. The 
following is the general state of calculations and of printing : — - 

The general form of the theory is drawn up, nearly in the 
same shape in which it was first exhibited to the Society 
(omitting for the present the terms depending on the Earth's 
oblateness and the change of the plane of the ecliptic), and is 
printed. 

The first step in the application of the theory is, to develop 
for the left side of each of the three theoretical equations (that 
is, the side which depends entirely on the actual place of the 
Moon, but without explicit reference to perturbing forces) all 
the successive steps leading up to that left side as derived from 
Delaunay's numerical values of the three co-ordinates ; which 
values are supposed to be not true, but so near to the truth that 
the squares of the corrections which they require may be neg- 
lected. This development is exhibited in numerical tables of 
great extent. There are 39 columns, each exhibiting a separate 
development as one of the steps towards the completed de- 
velopment of the left sides ; the terms of each column consist of 
multiples of sines or cosines with different factors and different 
arguments ; and the number of these terms in each column 
varies from 100 to 287, all carried to the 7th decimal. The 
whole of these results are printed. 

The next step is — supposing each of Delaunay's terms to re- 
quire a correction, which, before its magnitude is ascertained, 
must be used in the shape of a Symbolical Variation (S.V.) — to 
find the factors of these S.V. of Delaunay's terms, by application 
of which the S.V. of the terms of the left side of the equations 
will be formed. The theory of this transformation is printed ; 
all preparations for the transformation are prepared, and nearly 
all the work is done. 

It has been found desirable to abandon the use of the 
" Equation of Virtual Velocities,'* adopted in the first sketch of 



Peb. 1877. Fifty-seventh Annual General Meeting, xit 

tbe theoTj, and to substitute for it the "Equation of Radial 
forces." The addition which this change introduces into the 
Galcnlations is small. 

It wiU be seen, therefore, that the left sides of the equations 
^ very ueariy completed. The Astronomer-Royal contemplates 
the possible extension of some terms on which the more accurate 
moTements of the apse and node depend ; and, indeed; the work 
'^ been begun ; but it is not absolutely necessary for the prin- 
ciple of the general theory, and the extension is for the present 
«»pended. 

Of the right side of the equations, which contains the com* 
ptted perturbing forces, a large portion has been some time 
■"^ oompleted, and the Astronomer- Royal contemplates a very 
™7 devotion of the powers of the establishment to the compu« 
■■on of the whole perturbation-side, and to the exhibition of 
^detailed equations which contain the solution of the whole 
Irolem. 



^'Uction of the Observations of the Transit of Venus^ 

December 8, 1874. 

^the Annual Report of the Council last year, page 177, the 

■^**® ^r the Reductions was described in considerable detail. 

They have been continued thronghout' the year under Captain 

Tnpmaiij assisted by Lieutenant Neate, R.N., until November, and 

generally four computers. The great mass of the work, prepared 

on skeleton forms, has been done outside the Royal Observatory. 

Beferrijig to the headings of the last Report : — 

(i*) All observations with transit instruments, for local time 
^ longitude, are completely reduced. 

The longitudes of Honolulu and Rodrigues by the observa- 
^ong of the Moon in zenith distance, are completely reduced. 
P^se two calculations required the use of three millions of 
H^^eB. The zenith point of the vertical circle employed at 
"^^rignes was subject to variations not yet explained, and it is 
P^ible the longitude may require a slight correction. 

For Kerguelen's Island, chief station, the transit work, com- 
P^Hflons of clocks, latitude, and instrumental constants of the 
•^'tazimoth are reduced. The observed azimuths of the Moon, 
f^nt 130 in number, and each compared with a star, and the 
^^rpolations of the Lunar elements, are in hand. 

An element of great importance in the reduction of these 
'^gitudes is the amount of the correction to be applied to the 
lloon's Tabular Place. This is the subject of a separate com- 
iQanication to the Society by Captain Tupman, which will be 
printed in a future number of the Monthly Notices. 

(2.) The ditferences of longitude between the various stations 



i83 B^fxfrt of the Council to the . zxxni. 4» 

in the Hawaiian Islands and between Honolaln and San FrancJBeo 
are nearly oonolnded. 

(3.) The Greenwich Sidereal Times of every pbotograplif 
micrometrio measure, and other observation, in Egypt, Honolnlu 
and Bodrig^es, and of every photograph at Boorkee (Colonel^ 
Tennant's station) during the actual Transit, have been adopted, 
employing provisional longitudes for Honolulu and Eodrigaea 
founded on the meridional observations of the Moon. 

(4.) The whole of the calcnlations necessary to compare the 
proportions of Mr. De La Rue's material scale with its image as 
photographed 24 times by each of the five photoheliographs have 
been performed in duplicate, and the means of the resnlts have 
been taken for each picture. For two of the instruments, the 
computation of the distortion has advanced another stage — ^that of 
arranging it in angular directions around the centre of the fieM. 
In this work, 2,800 pages of ordinary foolscap size were closely 
covered with figures. There remains to dednce the curve of dis- 
tortion in the different azimuths, and to convert the resulte into 
a form convenient for application to the measures of the Solar 
photographs. 

(5.) Mr. G. E. Burton continued the measurement of the 
photographs until the end of April 1876, when, unable any 
longer to support the great strain upon his eyesight, he was com- 
pelled to abandon the work. During the seven months he was 
engaged upon it he made upwards of 38,000 bisections with the 
microscopes.* 

The following is a list' of the photographs of the actual transit 
measured by him : — 

Thebes (Egypt). — Ingress. 

34 square plates with Venus entirely within the Sun. 

28 small pictures f on a circular plate with Venus at in- 
ternal contact. 

55 small pictures on two circular plates, the planet being 
bisected on the Sun's limb. 

Honolulu. — Ingress, 

12 square plates with Venus approximately bisected on the 
Sun's limb. 

38 square plates with Venus entirely within the Sun. 

Kodrigues. — Entire Transit, 

24 small pictures {Ingress) immediately after external 
contact. 

23 small pictures (^Ingress) about the time of bisection. 

* We are happy to state that Mr. Burton, who is now First-Ai>sistaQt at 
Bunsink Observatory, has entirely recoverj-d. 

t By if mall pictures are meant those containing only t hat portion of the Sun's 
limb contiguous to the planet. On square plate* the Sun is alwjiys entire. AH 
the meafiurcmcnts are along the line of centres. 



Feb. 1877. Fifty-seventh AnntuU Oeneral Meeting. 183 

37 small pictures (Ingress) about the time of internal con- 
tact, Venus entire. 

35 small pictures (Ingress) just after internal contact, 
Venus entire. 

52 square plates durinf? transit. 

27 small pictures at Egress just before internal contact, 
Tentu entire. 

Bamham, New Zealand. 
13 square plates at Mid Transit. 

Kergnelen's Island. 
Attempts were made to measure 8 square plates (at Mid 
Trant'd\ bat tbe photobeliograph appears to have been hopolossl j 
out of focus on tbe day of tbe transit. 

Eoorkee. — Entire Transit, 

53 small pictures at Ingress. Venus approximately bisected. 
84 square plates during transit. 

7 square plates a,t Egress. Vetius approximately bisected. 

Melbourne. — Entire Transit. 

3 square plates hi Ingress. Fanf(« approximately bisected. 
26 square plates during transit. 

Sjdney, 11, S,W.— Entire Transit 
20 square plates during transit. Venus entire. 

>>len, '^.S.'TT,— Entire Traiisit, 
16 square plates. Venus entire. 

Woodford, 'N.S.W.— Entire Transit. 
20 square plates. Venus entire. 

Some 300 small pictures taken at Roorkee, Melbourne, and 
Sydney have not yet been measured; nor bave any measurements 
yet been made for the distortion of tbe instruments used at tbese 
•^ong, Eden and Woodford. 

(6.) The Tabular local distances of the centres of the Sun and 
yfnus as affected by parallax, and the factors of corrections to 
^"8*Mice for time and parallax, have been computed for every 
, pootograph, micrometric measure, and other observation of the 
•ctual transit in Egypt, Ilonolulu, Rodrigucs, and for every 
photograph at Boorkee. 

The work remaining may be briefly stated as follows : — 

Tbe completion of tbe longitudes of Kergnelen and Bumbam, 
*VZ., by the Lunar observations, and of Honolulu and dependen- 
^from San Francisco by chronometers, and of the distortion of 
toe five photoheliographs ; the determination of the distortion of 
^oe Indian and Colonial photoheliogmphs, including the measure- 
ment of the necessary photographs ; the measurement of the 
tniaining Sun pictures; the calculation of the local clenicuts 
^^ ^Vaimea and Kailua (Hawaiian Islands), Buruliam, N.Z., 



184 Eeport of the Council to the xxxm. 4* 

Xergaelen (3 stations), Melbonme, Sydney, Eden, and Woodford; 
and, lastly, the treatment of the results. 

It is impossible to form an even moderately acGoiate estimaU 
of the time which will be reqnired to finish all this work. II 
was hoped that more would have been done daring the paat year 
but uneroected delays occurred, one of which was a seciouBiU 
ness of Captain Tupman, which totally incapacitated him fen 
work for three months ; other delays are caused by the neoessit: 
which often arises of going again over work believed to be ire 
from error. 

It is not proposed to commence the printing until the ctlcm 
lations are further advanced. 



M. Le Verrier*8 Planetary JResearches, 

In the address of Professor Adams delivered at the last 

Anniversary Meeting of the Society, a complete abstract is givei 

of M. Le Yerrier*s planetary investigations as far as chapter zxiii. 

and now the Council have much pleasure in recording that at th( 

seance of the Academy of Sciences held on November 20, 1876 

chapters xxiv. to xxvii. of his Becherches Aatronomiquea wer 

communicated by him, containing the detailed explanations of th 

theories of VrauTis and Neytwits^ which thus complete his labc 

rious researches on the theories of tlie eight principal planett 

Tables of TJranus were presented in manuscript to the Academ 

at the same time. In this immense work M. Le Verrier ha 

been able to follow the same system throughout his invesUgf 

tions, owing principally to the long-continued series of planetar 

observations made at the Royal Observatory at Greenwich froi 

1750 to the present day, which have been reduced with grei 

order and precision, and made available for his purpose in bug 

a form as cannot be found elsewhere. M. Le Verrier remarl 

that since the discovery of Uranus in 1781, a very large numbi 

of accurate observations have been made ; and on account of ii 

small magnitude the planet has been observed with the san 

accuracy as a star. For this reason, the observations mac 

during the ninety-two years from 1781 to 1873 bave bee 

exclusively employed in the present investigation. In the con 

parison of the theory with the observations, the latter are repr 

Bented with the precision that might have been expected froi 

their small probable error. 

The Tables of Uranus and NeptunBy forming chapters xzyii 
and xxix. of the Recherches Astronomiqvss^ are both ready for M 
press, and the printing, it is expected, will proceed vnthout inte; 
ruption. The Council cannot refrain from offering to their di 
tinguished Associate their sincere congratulations on the net 
and successful termination of his great undertaking. 



feb. 1877. Fifly'tevenih Anntud Oeneral Meeting. i8j 



The NauHcal Almanac for 1880. 

In the NauHcal Ahnanac for 1880, an important addition baa 
been made to the list of standard stars, ordinarily used for the. 
determination of instrumental and clock-errors, the apparent 
fkbces of which are given for every ten days throughout the 
?ear. In observatories where observations are made at all 
DourB of the day and night, it is highly desirable that there 
should be a quick succession of clock-stars, not only for the 
conveDience of the observer in his ordinary work, but also in 
continuous unfavourable weather when the available time of 
observation ia frequently confined to the few minutes interval 
dnrinf^ temporary breaks in the clouds. This extended list will, 
tberefore, be found very useful in observatories where the ob- 
eenrations of stars are confined mostly to those for which 
apparent places are given in the Nautical Almanac. The new 
Stan have been selected principally from the Greenwich clock- 
star list, which is annually prepared for use at the Boyal Obser- 
tatorj, and freely circulated among the principal home, foreign, 
and colonial observatories. These additional apparent places of 
^ stars given in the Nautical Almanac for 1880 Will also be a 
gnat boon to the computer, who will in consequence be relieved 
of a considerable amount of daily calculation. Possibly at some 
fotnie time space will be found in the Almanac to include most of 
the stars in the Greenwich list ; meanwhile, astronomers are 
much indebted to the Superintendent for his very valuable and 
voluntary addition to our national ephemeris. As the standard 
stars have been well observed at Greenwich during the nine 
years from 1868 to 1876, it is hoped that the adopted mean 
)>laoe8 will be taken, as soon as possible, from the Nine-year 
^j(Mogue now in course of active preparation. 

Another important feature in the Nautical Almanac for 1880 
* the substitution of Le Verrier's Tables of Saturn for those of 
Bouvard, which have been in use since 1834. The now Tables 
We been communicated by M. Le Verrier to the Superintendent, 
^ anticipation of their publication. The tabular places of 
^ttm, as well as those of the Sun, Mercury, VentLS, Mars, 
•od Jupiter, are, therefore, now derived from Tables constructed 
by that astronomer. 



Solar Physics. 

The quiescent state of the Sun during the past year has not 
been favourable to physical investigations, but, notwithstanding 
^bis, some interesting results have been obtained in this branch 
^f astronomy. The Italian Spectroscopic Society* continues its 

* Memorie delta Sodttd dcgli Spettroscopuiti Italiani, 



x86 Be^ori of tlie Council to tlte xxxviL 4, 

work on the Solar prominences, and one of its most distingaished 
members, Professor Tacchini, has taken advantage of the lull in 
the activity of the San to discuss his observations of 187 1 and 
1873. A comparison of these two series shows that in 1873 the 
number of prominences had decrea^sed to one-half of what it was 
in 187 1, and that in both years twice as many were observed on 
the west limb as on the east. Further, there was in 1871 a pre* 
ponderance in the northern hemisphere, whilst in 1873 the pro- 
minences were pretty equally divided between the northern and 
southern, with a rapid diminution in number, for both years, from 
the equator towards either pole. In the present year Professor 
Tacchini finds that the height of the chromosphere has not 
diminished mach, and that the circulation of magnesium is aa 
active as ever, though hydrogen prominences and metallic erup- 
tions are now very rare. He farther connects the absence of 
sodium in the chromosphere with the present paucity of Sun- 
spots, and considers it likely that this element may have a large 
share in their formation. The granules and faculsB appear now 
to be very marked, notwithstanding the absence of spots. 

In partial opposition to this are Mr. Trouvelot's observations* 
on what he has called " veiled spots," from which he concludes-^ 

'* I. That during this year and especially during the interval 
from Jane 10 to August 18, and to a less degree to September 14, 
the chromosphere has been notably thinner than usual upon tlM 
entire surface of the Sun. 

'' 2. That the granulations have been smaller and less nnme- 
reus. 

''3. That the light-grey coloured background seen between the 
granules has been more conspicuous and has occupied more space 
than usual. 

'* 4. That there are spots which he has named * veiled spots, ' 
which are seen throngh the chromosphere which is spread over 
them like a veil. 

** 5. That these veiled spots are true openings of the photo- 
sphere, like those of the ordinary spots. 

"6. That daring this period these spots have been- larger, 
darker, and more numerous than he has ever before seen them. 

** 7. That the veiled spots are scattered throaghoat all lati- 
tades, thoagh more complicated iu the regions where the ordinary 
spots make their appearance. 

"8. That he has observed spots at least within 10° of the 
north pole of the Sun. 

** 9. That the flocculent objects sometimes seen projected on the 
umbra and penambra of spots are the remaining portion of the 
granulations composing the chromosphere, more or less dissolved 
by the forces emanating from the interior of the photosphere.*' 

Professor Langley has continued his discussion of the question 
of the relative amount of radiation from the Solai* photosphere, 

* American Journal of Scicnci ami Arts, No. 63. xi., March 1876. 



¥eb. 1S77. Ptfty-ieventh Annual Oeneral Meeting. 187 

sad from the umbra and penumbra of a spot respectively, and its 
bearing on the direct effect of Sun-spots on terrestrial climatos. 
An interesting paper by him on the subject will be found in the 
HoMy Notices for last November, and it will therefore be suffi- 
cient to mention, in this connection, that his observations show 
the nmhral radiation to be 54 per cent, and the penumbral Si 
per cent, of the radiation from the same area of photosphere ; from 
which he concludes that the greatest admissible direct effect of 
Son-^ts is to diminish the Solar radiation by a quantity some- 
what less than i-ioooth and somewhat greater than i-iiooth 
part, giving for the limits of possible direct effect on terrestrial 
eHmaie three-tenths and one-twentieth of one degree centigrade. 

k diaoussion has been made by M. Tisserand* of the observa- 

tiooB of the San, taken by Carrington's method at the Toulouse 

ObBenratory in 1874 and 1875, the result being to show that either 

Cimngton's or Spoerer's formula will satisfy the observations 

efficiently well, though the motions of some of the individual 

•pote are very erratic. M. Tisserand mentions particularly one 

which had such a rapidly increasing proper motion that after six 

^J8 its daily motion was found to have decreased by one- tenth 

of ita amount. Professor C. A. Youngt has attacked the same 

qnestion of the Sun's rotation, with the spectroscope, though 

'*ther with the object of verifying the principle of the displace- 

^t of lines in the spectrum, from the motions of the source of 

light, than with the idea of obtaining an accurate value of the 

I^fiod of rotation. From the relative displacement of thie D and 

^er lines at the east and west limbs respectively, he finds the 

^natoreal velocity to be i'42 miles per second, while direct 

ohaervation of Sun-spots gives 1*25. He is inclined to think that 

^ discordance indicates a physical fact, and that the solar 

Atmosphere really sweeps forward over the underlying surface in 

"^ 8^e way that the equatorcal regions outstrip the other parts 

of the Sun's surface. This conclusion is opposed to the results 

of the Greenwich observations, which are in remarkably close 

*P^ment with the received value of the Sun's rotation. 

Professor Young's observations were made with a fine dif- 
^tion gating by Mr. Rutherfurd, in which the spectra of the 
8Uth and eighth orders were observed, the difficulty caused by 
overlapping in the spectra of the higher orders being obviated by 
*he device of placing a prism in front of the object-glass of the 
""Jjcwing telescope, with its refracting edge perpendicular to 
•he lines in the grating. The red of one spectrum is thus seen 
Wow the yellow of the next, which in turn is below the green of 
^^^ sacceeding spectrum, and so on. With this ditt'raction 
•pectroscope Professor YoungJ has detected the duplicity of the 
'474 line in the Solar spectrum, the two components ' being 

* Cowptett Rendui, No. 14, Ixxxii., April 3, 1876. 

t American Journal of Science and Arts, No. 71. xii., November 1 876. 

I American JourmU of Science and ArtSj No. 66, xi., June 1876. 



x88 



Report of the Oounoil to the 



xxxni. 4, 



unequal. The coronal line corresponds to the stronger of the^ 
two, whilst tlie other is one of the faint lines in the spectnun oC 



iron. 



Discovery of Minor Planets. 

Thirteen minor planets have been discovered sinoe the lasft 
Annual Meeting. Though considerably less than in the preced- 
ing twelve months, yet the number is far above the general 
average of yearly additions to the group. The names of U^ 
planets and their discoverers, and the dates and places of their 
discovery, are given in the following table : — 



No. 

(160 
(161 
(16a 
(163 
(.64 
(165 
(166 

(167 

(i63 

^170 
(17. 
(.7* 



Name of 
Pbuiet. 

Una 

Athur 

Laurontia 

Erigone 

£\'a 

Loroley 

Bhodopo 

Uixla 

Sibvlla 

* 

Zvlia 



DiaooTcrer. 
C. H. F. Petera 
J. Watson 
Prosper Henry 
PeiTotin 
Paul Henry 
C. H. F. Peters 
C. H. F. Peters 
C. H. F. Peters 
J. Watson 
lV>sj>ep Henry 
Pernnin 
Ik»prelly 
Borrelly 



Date of 
Diaoovery. 

1876 Febroaiy 21 
April 18 
April 21 
April 26 
Jnly 12 
August 10 
August 17 
August 29 
September 28 
September 28 

1S77 January lo 
January 13 
February 5 



Place of 
Dlacorerj, 

Clinton, U.& 
Ann Arbor, U.Sb 
Paris. 
Toulouse. 
Piuris. 

ainton, U.S. 
Clinton, VJS. 
Clinton, U.S. 
Ann Arbor, n.SL 
Paris. 
ToulouBo. 
Marseilles. 
Marseilles. 



The following six minor planets, the discoveries of which 
woro nx*or\iiHl in the two preooding Reports, have been named 
during the jVist yeiur : — 



Niv v»>»> 


Juewa. 


No. ^«5o) 


Nuwa. 


.. v»**> 


liallia. 


,. (»54) 


Bertha. 


.. v'*^^ 


Meiiusa. 


.. v»-^-^^ 


SCTIU. 



It is At length fonnd impossible to continue the compatatikm 
of the op(H>sition ephemeridoA usually inserted in the Berliner 
/<iAr6ifoA tor all the ^mall planets which come into opposition 
during the year. Sjvict* has only been fonnd for fifty out of 125, 
which will Iv in op|vsiiion Iviwtvn January i and December 
31, 1877, Mi^t of the plan»^tv« si^leotovi are of small magnitude, and 
the ol^wrvatious nnist^ therefore, for the m*^t part, be coniiDed 
to thivM^ made with lar^^^ ix^uatoreals, for it is found to be waste 
of time to look for tiic &auallest of thc60 planets with the preGent 



Feb. 1S77. Fifty'Seventh Annual General Meeting, 189 

meridional instraments. For this reason it is to be regretted that 

10 few of the older and larger planets are not included in the 

selection. In 1877, though twenty-four brighter than the tenth 

Sttgnitade are in opposition, only eight of them, iucluding the 

iooT senior planets, have a daily ephemeris ; and, consequently, 

nxteen of liie brightest cannot be observed on the meridian 

daring this year. 

From an examination of the Table of opposition-magnitudes 

girenfor this year in the Berliner Jahrhuch for 1879, it will be 

Ken tiiat by taking the means of groups of twenty-five con- 

ncative planets ranged in the Table in the order of their dis- 

corery, the lowest limit of magnitude has been, on the average, 

ntcbed. In the Table, 125 opposition magnitudes are given. 

Forming these into five groups, the mean magnitudes are respec- 

Wy 9*6, I I'D, 1 1 '4, 11*4, and 11*3, and by subdividing the 

fat group into two groups of ten and fifteen, the respective 

BMoi magnitudes are 87 and lo'i. It has also been found 

^ wben the same planets are ranged in the order of their 

iBeiii distances from the Sun, the corresponding means bear 

a smiilar relation to each other. 



Discovery of a New Comet, 

•Aft^r an unusually long interval since the detection of a 
''^^^ <Jomet, M. Borrelly discovered one at Marseilles, early in the 
nonuiig of February 9, 1877, in the constellation Ophruchis. 
Its observed position at 3** 41™ a.m., mean time at Marseilles^ 
^R-A. ly^ 13™, and N.P.D. 91° 17'. Its motion was rapid, 
increasing daily 44" in R.A., and 3° f towards the north. It 
Jw a bright and round nucleus about 3'*5 in diameter.* The 
^ discovered comet of unknown period was detected by M. 
^^"^%, on December 6, 1874, 



jyArrcsVs Periodical Comet, 

hi the CompUis Bendus (No. 9, Aout 28, 1876), M. Leveau 
*** given the final osculating elements of this interesting periodi- 
^ comet, resulting from the investigation of which a brief 
*7^t is given in the last Annual Report. This comet was 
d^vered by M. D'Arrest, at Leipzig, on June 27, 185 1, and will 
^ in perihelion in May next. M. Leveau's investigation is based 
^ the observations made at the former apparitions in 1851, 
^^57} And 1870, and he has previously published elements for the 

* The anDonneement of the diBCOvery of this comet was received by 
f^hgnm from M. Stephan on the day of the Annual Meeting, in time to be 
•■•wtcd in this Report. The comet was independently observed by M. C. F. 
iWhole, At Copenhagen, oq the following morning. — K. D. 



•196 » B^ort of the Council to the xxxvn. 

epoch 1869, October 13. By applying the perturbations p 
dnced by Jtvpiter^ Saturn, and Mars, from this epoch to 18' 
January 14, he has dedaced the following corrected elemei 
from which a working ephemeris has been calcalated for 1 
convenience of observers at the approaching apparition. 1 
now escalating elements are : — 

Epoch 1877, January 14*0, M.T. Paris. 



// 



f = 301 56 54-42 

w = 319 9 1470 

y Mean Equinox and Ecliptic, l88o*o. 

e> « 146 9 2763 ^ ^ *' ' 

♦ = 15 43 9'22 
^ - 38 53 1804 
n « 540"-4ioo3 

Perihelion passiige, 1877, May 10*339, M.T. Paris. 

The details of M. Lovoaa's investigations will be published 
the Annates de V Ohservatoire de Paris, 



Santiago de Chile Observations, 

The observations made with Ihe Meridian- Circle of t 
National Observatory at Santiago de Chile from 1856 to i8( 
have lately been published under the superintendence of i 
former Director, Dr. C. W. Moesta, who had undertaken this di 
since his return to Europe. They are contained in Vol. II. of 1 
Santiago Astronomical Ohservatuytis, and are given in the form 
a catalogue consisting of 3,309 stars, mostly south of the equat 
The reduction of the observations from apparent to mean pb 
is given in detail for each star, and the mean Right Ascensic 
and north polar distances for 18600 for each separate obser 
tion. The results are, therefore, not so available for general i 
in this shape as they would have been if they were collect 
the means taken, and then formed into an ordinary catalog 
of stars. But from the orderly manner with which the sepan 
results are arranged, there is not much difficulty in forming, 
required, a mean result for the epoch i860, January i. 

The volume also contains observations of the Moon a 
Moon-culminating stars from January 15, 1856, to December , 
1857, and also some observations of Mars^ Ju]}iiery Saiu 
Uranus, and Neptune, an4 of a few of the minor planets, mt 
principally in 1856. The volume, which was printed at Dresdi 
concludes with a comparison of the Santiago Catalogue w: 
those of Washington, Johnson, and Taylor. 



Feb. 1877. Fifty'ievenih Annual General Meeting. %gt 



Physical Observations of Saium, 

Mr. Trouvelot* has during the last four years had many 
opportaDities of examining the planet Saturn, nsing the 15- 
mch refractor of Harvard College, the great Washington re- 
fractor, of 26 inches aperture, and the 6-inch refractor of 
his own Observatory, and from the observations thus made he 
has drawn the following conclusions, A and B denoting the outer 
and inner divisions of the outer ring, and G the outer portion of 
the interior bright ring : — 

"i. That the inner margin of the ring b limiting the outer 
horder of the principal division, has shown on the ans€e some 
BBgnlar dark angular forms; which may be attributed to an 
ini^alar and jagged conformation of the inner border of the 
ring B, either permanent or temporary. 

*' 2. That the surface of the rings A, B, c has shown a mottled 
or cloudy appearance on the ansod during the last four years. 

"3. That the thickness of the sjstem of rings is increa»ng 
from the inner margin of the dusky ring to the outer border of 
the ring c, as proved by the form of the shadow of the planet 
thrown upon the rings. 

"4. That the cloud-forms seen near the outer border of 
the ring c, attain different heights and change their relative 
position, either by the rotation of the rin^ upon an axis, or by 
fome Jocal cause; as indicated by the rapid changes in the 
^dentation of the shadow of the planet. 

"5. That the inner portion of the dusky ring disappears in 
the light of the planet at that part which is projected upon its 



"6. That the planet is less luminous near its limb than in 
more central parts, the light diminishing gradually in 
approaching the border. 

"7. That the dusky ring is not transparent throughout, 
contrary to all the observations made hitfierto; and that it 
pow8 more dense as it recedes from the planet; so that, at 
■hont the middle of its width, the limb of the planet ceases 
^rely to be seen through it. 

"8. And, finally, that the matter composing the dusky 
'^gis agglomerated here and there into small masses, which 
almost totally prevent the light of the planet from reaching the 
^0 of the observer." 

Astronomers are much indebted to Mr. Marth for the con- 
tinnation of his ephemerides of the satellites of Satnm, No ob- 
^rvations have, however, been communicated to the Society 
*^ the year. 

* American Journal of Science and Arts^ No. 66, xi., June 1876. 



Xg2 Report of tJi^ Cotmcil to the xxxyit. 4« 



Observations of Jupiter's Satellites at Adelaide. 

Mr. Todd has employed his new S-inch eqnatoreal, by Cooke, 
monnted in December 1874, in making a very valnable series of 
observations of the phenomena of Jupiter's satellites daring the 
last opposition of the planet, extending from Jnne 13 to October 
15, 1S76. He has recently forwarded to the Astronomer-Royal, 
for commnnication to the Society, a detailed statement of these 
observations, which consist of eclipses, occnltations, and transits 
of the satellites, and also of the ingress and egress of the shadows. 
The local mean times of observation are given, as well as the 
corresponding Greenwich mean times, which are compared with 
the cfdcalated times in the Nautical Almanac, Some notes on 
the physical appearance of the planet accompany the observations. 
A very interesting phenomenon observed more than once, in- 
dependently, by Mr. Todd and by his assistant, Mr.Bingwood, 
occurred when a satellite was on the point of occnltation. 
Instead of disappearing gradually behind the planet, it was 
apparently projected on the disk, as if viewed through the edge 
of the planet, supposing the latter were surronnded by a' trans- 
parent atmosphere laden with clonds. This curious phenomenon 
was noticed on two occasions at the disappearance of the first 
satellite, when it was thus distinctly visible on, or through the edge 
of, the disk, for about two minutes before it was finally occulted. 

Mr. Todd bears witness to the constantly varying aspect of 
the surface of Jupiter. He was much impressed with some 
sudden and extensive changes in the cloud-belts, as though a 
violent storm was raging, changing their appearance within an 
hour or two, or even less, not only in their form, but also in 
their magnitude. 



DrtuciHijs of Jujiiter. 

Considerable attention has been directed during the last few 
vears to the apparent changes on the surface of Jupiier^ and a 
large numbt^r of careful drawings have been made from time to 
time. Some of those have appeared in the Monthly Notices^ in- 
eluding the two interesting series communicated by the Earl of 
Bosae and Mr. Knobol. Following a suggestion of Dr. Lohse, 
of Berlin, the Council appointed a Committee for the examina* 
tion of all drawings forwanieil to the Society. In reply to a 
circular issued by the Committee, drawingrs from widely separated 
places have betni rtHxnved, and these have been or will be sent 
to Dr. Lohse, a member of the Committee, who has undertaken 
the collation of them. Forty-two delineations of the planet have 
been received from Mr. Hirst, of Sydney, and also a series of 153 



Feb. 1S77. Fifty'Seventh Annual General Meeting, 195 

I 

drawindfs from Mr. Tronvelot, of Washington. Others have been 
forwarded by Profesflor Tacchini, of Palermo, Mr. Todd, of 
Adelaide, and M. Lebardelay, of Fontenay-le-Marmion. These 
dnwings all show that very rapid changes are still going on apon 
the 8Qr&ce of JupUer^ though the character of the eqnatoreal 
markings differ slightly from those shown upon the drawings of 
the phnet made two or three years ago. 



We Supposed Viacovery of the Object perturbing the Motion of 

Procyon, 

h former reports allnsion is made to the observations of an 
<^ supposed by M. Strave to be a companion to Procyon, 
>Bd which seemed, from a comparison of his observations with 
fc theory previously deduced by Dr. Auwers, to be the object 
CMuing the observed irregularities in the proper motion of this 
1^. The image of this supposed satellite is now found by 
U. Stmve to have been produced by an optical illusion on his 
put, and also by his assistant, Herr Lindemann. 

As long ago as the year 1844, Bessel remarked that the proper 
"wfcions of Sirius and Procyon were subject to irregularities, 
which he conjectured must be due to the attraction of bodies in 
*^ vicinity, either not perceptible to us, or which, at any 
nte, had not yet been discovered. It is not necessary to allude 
"^her to the case of Sirius at the present time ; but as regards 
"rocyon the matter was put into a definite shape by Dr. Auwers, 
who in the year 1861 made a careful investigation of all the 
available observations, and showed that it was possible to recon- 
^ the whole by the hypothesis that the motion of the star was 
"i«tnrbed by the attraction of an unseen object, about i"*2 
y^^tant, round which it moved in a plane perpendicular to the 
jj^ of sight, and in a nearly circular orbit, in a period of about 
forty years. For some time before this M. Otto Struve had been 
examining the star with the Pnlkowa refractor, continuing his 
•crutiny without result till the 19th of March 1873, when he 
"•tected a very faint point of light following the star at a very 
^^ distance, nearly in the same parallel. As the point of 
'%Qt Was also seen by his assistant, Herr Lindemann, M. Struve 
^•8 confirmed in his belief of the objective nature of the phe- 
^^l^non. He was, however, desirous that the suspected object 
f«ould be looked for at other observatories possessed of sufl&cient 
^pnmental power. He communicated his wish immediately to 
*'• Kewall, requesting him to turn his Cooke's 25-inch refractor 
'^pon it, but unfortunately Mr. Newall was absent at the time, and 
^jlight soon afterwards prevented further investigation till the 
^xt spring. Meanwhile Dr. Auwers repeated his theoretical in- 
Teitigation, and calculated what change the apparent position of 

p 



194 Beport of the Council to the 

the object ought to undergo in that time, supposing it to be 
really the disturbing cause of the proper motion of Procyon, The 
months of February and March 1874 were singularly un&Yonr- 
able for astronomical observations owing to bad weather, but on 
the 9ih of April and subsequent days the point of light was again 
seen, the observed position-angle corresponding with what Dr. 
Auwers had theoretically found that it should be. 

Before these observations of M. Struve the star had been 
examined with the 2 6 -inch refractor at the Washington Observa- 
tory, but without detecting a companion ; however, on the 1 2th of 
November 1874, Mr. Alvan Clark thought he saw a small ol^ect 
in a different position from that seen by M. Struve, and on Novem- 
ber 25 and 26 of the same year Professor Holden saw another 
object within 10'' of Procycru, and also at a different position- 
angle from that seen at Pulkowa. On January 12, 1876, he and 
Professor Watson both saw this, and also two other faint points 
of light, all less than 10" from the star, and at different position, 
angles, both with respect to each other, and also to thai 
announced by M. Struve. Professor Holden suspected a still 
fainter companion between one of these and Procyon, These 
additional observations induced M. Struve to re-examine th< 
subject with great care, the result of which has been to convina 
him that the phenomenon he had seen had no objective existence 
but was the c^ect of an optical illusion which cauf^es him (anc 
Herr Lindcmann also) to see under certain circumstances a fain 
image, or point of light, at about 10" distance from a bright star 
and nearly in a horizontal line with it. On the 17th and i8tl 
of April 1876, he found this to be the case with the bright star 
Reguhis and Capella. On the i ith of the following month, botl 
he and Herr Lindemann observed a similar point of light nea 
Ardurus, which, however, they were unable to perceive i&gain oi 
the following night. 

M. Struve intends to make some farther experiments on th 
subject, as a warning against a species of optical illusion whic 
has not hitherto received much attention. It is a very singula 
circumstance that the different position of Procyon in the telescop 
with respect to a vertical circle seems to have produced thf 
apparent change of position-angle in the supposed satellite wbicl 
from its agreement with the theoretical investigation of D 
Auwers, led M. Struve so strongly to believe that he had detecte 
the body whose attraction was producing the observed variabilit 
in the proper motion of Procyon. 

It is certainly more pleasing to record the confirmation of 
supposed discovery than its withdrawal ; yet the latter has oc« 
sionally to be done, as in the case of the unconfirmed satellites < 
Uranus, generally believed to have been seen by Sir W. Hersche 
until disproved by modem observations. The present instance : 
interesting as showing the close scrutiny to which any astn 
nomical observation is now subjected by the aid of other instn 
ments of equal or greater power, and the consequent iniprobabilit 
of anything not really objective being long supposed to be so. 



F«:?lb. 1877. Ftfly-seventJt Annual General Meeting, 195 



Photogrofhs of Spectra of Sta/rs, 

In an oral oommnmcation to the Society at the December meet- 

_r> givinff the snbstaDce of a paper presented to the Bojal Society, 

OUT President, Dr. Huggins, gave an acconnt of the important 

Tosnlts he had obtained in the application of photography to the 

vpeotm of stars, a work which he nrst took up in conjunction with 

Dr. Miller in the year 1863. Dr. Hnggins has obtained successful 

photographs of the spectra of Sirius^ Vega, Venus, and the Moon, 

with comparison spectra of the Sun, taken the next morning on 

^ 8une plate. The spectrum of Vega in particular shows seven 

itroDg lines in the ultra-violet extending from a to m of the Solar 

ifeetmrn, and these are so well defined as to allow of accurate 

nioomebric measurement. Dr. Draper has also for some time 

put been engaged on the same work, and has obtained photo- 

j^hs of Vega and AUair, showing bands or broad lines in the 

^t and ultra-violet regions, unlike anything in the Solar spec- 

^'un. He has also taken photographs of the spectrum of Venwf, 

which show a weakening towards H and above that line of the 

*^B character as that which he has photographically observed to 

^ pUce in the spectrum of the Sun near sunset. 



New Double Stars. 

A catalogue of fifty new double stars, discovered with the 
'I -inch refractor of the Cincinnati Observatory, has been circu- 
f^ted by Mr. Ormond Stone, the Director, It has been prepared 
^7 Ur. H. A. Howe, who has arranged the matter in a tabular 
^d convenient form for reference, exhibiting the approximate 
^A. and N.P.D. for 1880, with the precessions in both elements ; 
^0 estimated position-angles, distances, and magnitudes of the 
^Diponents ; and the date of the discovery of the duplicity of 
*he star. The stars are included between 8° and 40** south decli- 
'^on, and the angular distances vary from less than one second 
^ eight seconds of arc. The greater number of the stars are of 
••JWill mag^tude, averaging 8 and 10 for the two objects. A few 
^^the principal components are of the sixth magnitude, while the 
***^e8t are registered as of the eleventh. 

. Mr. Bumham has continued his examination of the heavens 
JJth the view of detecting close double stars not before identified. 
I^W he has succeeded in this interesting field of research can 
** gathered from the catalogues of new objects the duplicity 
?' which has been first noticed by him. These have appeared 
*^ various publications — first, in our own Monthly Notices, and 
"^hgequently in the Astronomische Nachrichfen and the Awe^ 
"''ttn Journal of Science and Arts. It would have been more 

p 2 



196 Report of the Council to the xxxrn. 4, 

convenient to those who are in the habit of referring to previoas 
resnlts of donble-star observations if a continuous series of cata- 
logues, such as those of Mr. Bumham, had appeared from time to 
time in the same publication ; and as the commencing catalogues 
of his series of measures are inserted in the MorUMy Notices^ some 
regret has been expressed that all of them had not been com- 
municated to the Society. 

From the large number of hitherto unknown double stars 
discovered by Mr. Bumham and other recent observers, it may be 
concluded tbat as their attention is now directed to the smaller 
classes of stars, it will be found that, like the minor planets, an 
almost inexhaustible field of discovery is open to any one having a 
good eye and a suflSciently powerful instrument. It is, however, 
important in the case of suspected binaries, that the angular 
positions and distances should be instrumentally measured, if 
possible, as mere estimated data should not be considered suffi- 
ciently accurate as the basis for any future determination of 
their orbits. 



Micrometric Measures of Dotible Stars. 

M. Dun^r has recently published an important series of 
observations of double stars made at the Imnd Observatory in 
the years 1867 to 1875, in the course of which nearly 2,700 
observations have been obtained of some 600 stars selected 
chiefly from W. Struve's catalogue. The measures were made 
with a filar micrometer applied to a Fraunhofer equatoreal of 245 
millimetres (about 9^ inches) aperture, and 4*3 1 metres (about* 
14 feet) in focal length, and the periodic errors of the screw wer9 
carefolly determined in 1876 at the end of the series of observa- 
tions. Besides his own measures of distance and position-angle, 
M. Dun6r has collated, under the head of Notes, at the end of 
the volume, the principal results obtained by previous observers, 
and has exhibited, in a tabular form, the changes which appear to 
have taken place, as shown by diHcordances from the mean. In 
a final table, a classification of the stars, according to the amount 
of relative motion of the components, is given, the largest class 
being that containing double stars which have not as yet 
changed their relative position. M. Dun6r is still continumg 
bis work on double stars, to which he hopes to be able to devote 
a much larger portion of his time than has been possible in the 
period to which these observations refer. 

The following table, according to M. Duner, shows the distri- 
bution of stars, with reference to their relative motion, since the 
date of the first observations: — 



Feb. 1877. Fifty^geventh Annual General Meeting. 197 



ClaaB. 


notion. 






Number of Stan. 


I. 


360 




S 


n. 


180 




S 


lU. 


90 




8 


IV. 


30 




16 


V. 


10 




46 


VL 


Certain 




55 


vn. 


Probable 




51 


VTTT. 


Insensible 


as yet 


207 


w. 


NIL no ph] 


rsical com 


aexion 1 1 



A memoir by Mr. Knott, containing nearly 2,000 observations 
of about eighty selected double stars, has been lately communi- 
cited to the Society, and will be published in the Memoirs, In 
^ careful work Mr. Knott has followed the excellent model of 
the Cefe«<2aZ Cycle, accompanying his results by descriptive and 
cntical notes, in which (as also in M. Duner's volume) particular 
ftttention is paid to the colour and magnitude of the components. 



Doherck'a Neto Elements of the Orbit of w Leonis. 

In a paper read before the Royal Irish Academy in April 
» Dr. Doberck has given the result of his recent investigation 
®* the orbit of ut Leo^us, in which he has discussed with great 
'^Qipleteness all the data at his disposal up to 1876. This star, 
^^e of the most remarkable of the double stars discovered by 
^^ W. Herschel, has occupied the attention of most of our 
double-star observers since its discovery, but its excessive close- 
ness bas made it a very difficult object to measure. For this 
'^^n, very great discrepancies are found in the observations, 
^pecially when they have been attempted with small telescopes. 
Notwithstanding these difficulties, the star has been carefully 
^tched during the last fifty years, or from the time when 
*' • Struve commenced his observations at Dorpat. The notes 
01 tbe appearance of the two stars recorded by the different 
observers are very conflicting, for while Sir James South, in 
'026, states that the components are of the sixth and ninth 
^■J^gnitudes, the small star being pale blue, W. Struve, about 
^be same time, remarks that they differ but little in magnitude 
*nd are both yellow, the smaller being certainly of the deeper 
colour. On the other hand, M. Derabowski has more recently 
^ade them white. The change in the relative distances between 
*"© stars was noticed by Sir W. Herschel, who made notes in 
^782 and 1783, that the distance between them was increasing; 



198 Report of the Gomicil to the XXXVil. 4, 

in 1795, ^^^ ^^^y were half a diameter of the smaller star 
asander; and in 1804, that the space between them was nearly 
a diameter of the smaller one. It was seen oblong by W. Struve, 
in 1836 and 1838, and single by Madler in 1843. Winnecke, in 
1858, and Engelmann, in 1865, were unable to separate the two 
objects. 

Elements of the orbit have been calculated on several 
occasions, bat no one has paid greater attention to this star than 
Professor Klinkerfues, of Gottingen. But the great difficulty 
experienced in obtaining accurate measures has created corres- 
ponding difficulties in the calculation of the orbit. A first inves* 
tigation of Klinkerfues appeared in 1855 (Ast. Nach, No. 990); 
these were followed in 1858 by a second and revised system of 
elements (Ast, Nach, No. 1,127), both of which were intended to 
illustrate his method of determining the orbit of a binary star; 
and, lastly, in his Theoretische Astronomies he has published a 
third series of elements determined on twelve annual means of 
measures made to 1867, by Herschel, W. Struve, Madler, Secchi, 
and Engelmann. In determining these last elements, Professor 
Klinkerfaes considered that he had used all the available 
measares, but Dr. Doberck points out that many additional 
measures had been made at the time, though many of them have 
only recently been published. 

That the elements calculated by Professor Klinkerfues were 
imperfect, and required considerable modification to satisfy the 
observations, was very evident to those interested in the 
subject, as may be seen from the following remarks of, M. Otto 
Struve: "The elements of the orbit of u> Leonis^ calculated by 
M. Klinkerfues, in 1858, are still very defective. For 1870 hm 
cphemeris indicates the distance as i'''o6, and the direction as 
io°'9, while our measures give respectively o'''58 and 52**. 
Probably the erroneous result of his calculations should be 
attributed chiefly to the uncertainty of M. Madler's measures, 
wliich were employed to form the last normal place for 1853. 
Without doubt the period of revolution will turn out to be much 
shorter than that found by M. Klinkerfues." 

Dr. Doberck, at the commencement of his investigation, 
selected the angles and distances observed by O. Struve, to form 
his interpolating carves, and thus construct an ellipse. He 
found all the points well represented, but the principal star was 
not included in the circumference, and he was not able to alter 
the curve in a justifiable manner, so as to get the star inside the 
ellipse. He " considered it therefore not unlikely that O. Stmve's 
measures, though as accordant among themselves as could be 
expected from the large refractor, were perhaps not quite freb 
from systematic errors, though corrections had been applied as 
deduced from observations of artificial double- stars." By this 
system of interpolating curves applied to all the observed angles 
and distances, and by varying them when required to satisfy 
the observations, Dr. Doberck has determined five different sets 



'^ly. 1&77. FiftysevetUh Annual General Meeting, 199 



ot elements, of wliich the 


following 


are the last and definitive 


v&Laes: 






/ 


Node 






148 46 


7 






64 5 


A 






121 4 


e 






0536 


P 






110-82 yean 


T 






1841-81 


a 






o"-890 



A comparison of the observed angles of position and distances, 
vith those dednced from the preceding elements, is given, includ- 
ing all the known observations from 1782 to 1876. The residual 
ORon appear small, and good evidence is shown that the 
neasnres are represented more closely by Dr. Doberck's new 
fi^nts than by any of those previously published. 



Dan Echt Observatory Publications, 

^ble-star observers will be thankful to Lord Lindsay for 
the publication of the first volume of the Dun Echt Observatory 
publications, which contains a summary or index of all the 
"Wurements of double stars included in W. Struve's Mensurce 
^^crotnetriccB and appendices. Tho scarcity of the original 
▼wume, which is rarely found in the libraries of amateur ob- 
^Tera, together with its inconvenient size, has induced Lord= 
*^dsay to commence his series of publications with this very 
^^laable and useful abstract, in which most of the information 
^'ftting to Struve's measures is given. The compilation, and 
*n^ngement of the catal<?gue, and the reduction for bringing up 
^''e epoch to 1875, have been performed by Dr. R. Copeland. 

The separate columns of the catalogue contain the B. A. and 
^lination for 1875 ; the lowest and highest powers used by 
otruve ; the mean date of observation ; the mean distance and 
Mtion-angle as deduced by Struve ; and the magnitudes and 
^loursof the components ; the latter translated from the Latin 
^J^oies. These translations of the colours were carefully con- 
f^^lered, and then strictly adhered to. A table of the precessions 
^ (leclination for ten years is also appended ; and a diagram is 
P^PD, from which the variable part of the precession in R. A. for 
^ years in minutes of time can be taken. The work is printed 
"^.ciaarto form, and has been most liberally distributed by Lord 
l^dsay among astronomers and bcieutitic institutions. 



200 Report of the Council to the XIXTIL 4, 



The New Star in Gygnus. 

A remarkable stellar outburst, similar to that which appeared 
in Gorona Borealis in May 1866, was first noticed by Dr. 
Schmidt, at Athens, on the 24th of November last, at 5.41 p.m., 
in the constellation Cygnvs, then near the zenith. The new star, 
when first observed, was of the third magnitude, and of a yellow 
colour, near p Gygni, where Dr. Schmidt is sure that no corres- 
ponding object existed on the evening of November 20. The 
sky was overcast at Athens on the three following days, and 
most probably the outburst appeared at its full brilliancy in the 
interval between November 20 and 24. At midnight on the 
latter day the light of the star was of greater intensity than thai 
of 17 Pegasiy noted of the third magnitude by Argelander. Its 
position does not appear to be recorded in the usual catalogues of 
small stars ; certainly not in those of Lalande, Weisse's Beesel, 
Bode, D'Agelet, or in the Durchmusterung of Argelander. From 
an observation made by Mr. Hind at Mr. Bishop's Observatory on 
December 13, its R.A. for 18760 is 21** 36™ 5o'*4i., and its 

N.P.D. 47^43' 2i''-5. 

Unfortunately, Dr. Schmidt's discovery was not immediately 

communicated to the Astronomer-Boyal or to any other English 
astronomer, although a telegram was sent to Dr. Littrow, ai 
Vienna, and probably to other Continental observers. The first 
information of the sudden appearance of the new star was only 
received in England in the second week in December, from the 
public notices inserted in the Bvlletin Intern atimial and Compiet 
Rendus, This neglect is much to be regretted, as there were 
eight favourable evenings at Greenwich before December 9, when 
spectroscopic observations might have been successfully noiade, 
and of these at least two were near the time of the star's 
maximum brilliancy. Principally for this reason, but also ia 
consequence of almost continuous unfavourable weather after- 
wards, very few observations of the star have been made in this 
country. When seen by Mr. Hind on December 1 3, it had receded 
to the sixth magnitude, and was without a trace of colour. 
The observers in Paris were more fortunate in obtaining informa- 
tion, for the star was examined on December 2, during a brief 
interval of clear sky, by MM. Henry, Coruu, and Cazin, and 
estimated of the fifth magnitude. Under more favourable cir- 
cumstances, on December 4, M. Comu made some satisfactory 
observations of the spectrum of the star with the eastern 
equatoreal of the Paris Observatory, the magnitude on that day 
being estimated at 4-5. The spectrum exhibited eight detached 
bright lines on a luminous ground, with an almost complete inter- 
ruption of the light between the gi*een and the indigo. M. 
Comu saw no dark lines ; if they had existed they must have 
been very fine, and invisible owing to the faintness of the light. 
Naming the bright lines according to their intensity by the 



Feb. 1877. FiJty^evefUh Annual General Meeting. 201 

Greek letters a to 0, their poeitions in the spectmin, in relation 
to thuse of certain elements, may be readily seen from the num- 
bers in the following table determined by M. Comu : — 





a 


8 


7 




3 


c 


n • 


ff 


Obnnred 


661 


588 


531 




S17 


500 


483 45" 


435 


Hjdrogen 


656 (C) 


• • • 


• • • 




• • • 


• • • 


4«6(F) ... 


434 




• • • 


589 (D) 


1 ... 




• • • 


• • • 


• • • • • • 


• • • 


MigDeQQm 
OonulIiDe 


• • • 
• • « 


• •• 
• • • 


• • • 

532 


{h 


517 
mean) 

• • • 


• • • 
• • • 


• • • • • • 

• • • • • • 


• • • 

• • • 


Cbonoiphere 
liBes. 


• • « 


587 


• • • 




• • • 


• • • 


447 


• « • 



M. Comn remarks as an interesting fact, bat one requiring 
tthfirmation, that there are several coincidences shown in the 
pnoeding table which have led him to the conclusion that the 
iv^t lines in the star-spectrum correspond exclusively with the 
principal lines in that of the chromosphere, and therefore that the 
%lit of the star possesses precisely the same composition as that 
rf the Solar envelope. He says : " But the most curious result, 
^h I give here with much reserve, but which it will be very 
interesting afterwards to verify, is the coincidence of the line y, 
T«y bright in the spectrum of the star, with the green line 
^= 532 (^474 o^ KirchhoflTs scale), observed in the spectrum of 
ti» Solar corona and in the chromosphere ; the feeble band 6 
fwregponds also with a band X = 447 of the chromosphere ; one 
V thoB led to think that the liner corresponds rather with the 
^sigbt line of the chromosphere X ^ 587 (helium), than with 
^ of sodium, 589. If this interpretation be correct, the bright 
"IKS of the spectrum of the star comprehend exclusively the 
Brightest and the most frequent lines of the chromosphere.'* 

The spectrum of the star has also been examined by Padre 
Secchi, Dr. Vogel, and others, all of whom confirm generally the 
prwious observations of M. Cornn. Several bright lines were 
•en bj Dr. Vogel in the red, blue-gi*een, and blue parts of the 
■pcctrum ; bright bands were also visible in the yellow and green ; 
wt these may possibly be portions of a continuous spectrum 
■WD bright by contrast with absorption bands, of which there 
^ere as many as eight or ten. The blue and violet were brighter 
than in most stars with band spectra. The bright lines c, f, and 
Dj were visible ; 6, however, was probably not seen bright, but a 
hright line on the blue side was noticed, which may possibly be 
^entical with a line which under peculiar circumstances is the 
hnghtest in the spectrum of hydrocarbon. One seen in the 
▼iolet may be the third line of hydrogen. Dr. Vogel remarks 
wat there are three other stars in Cygnus giving quite unique 
spectra. 

% careful comparisons with several neighbouring stars, Dr. 
Schmidt noted the gradual diminution in the intensity of the 



202 Beport of the Council to the xxxni. 4, 

light of the star almost daily. The variations of magnitude 
exhibited in the following table : — 

November 24 3*0 Magnitude. December 5 59 Magnitude. 

7 6-3 



»» 


25 


31 


»> 


»> 


26 


31 


»» 


♦ » 


27 


32 


»> 


>» 


2$ 


3-8 


»» 


t» 


29 


47 


»» 


»» 


30 


50 


1* 


December 


I 


52 


■»! 


»» 


2 


54 


»t 


tf 


3 


5-6 


»» 



tt 
*f 

10 6-5 

11 67 

12 67 

13 6-8 



8 6-5 

9 6*6 

10 6-5 

11 67 

12 67 

13 6-8 

14 69 

15 70 



»» ••!• « :7 t» 



ff 



4 5-8 



>» *!■ J " »» 



At the end of the year the star was still about the fleventh 
magnitude, and of a decidedly orange colour, with a reddish tint 



Siiifjyected Changes in Nehula Messier, No. 1 7 (the Horseshoe 

Nebula). 

Professor Holden has made a very interesting comparison of 
all the available drawings of the well-known nebula MeBsier, 
No. 17,* with the object of ascertaining whether any visible 
changes could be detected in the relative positions of the nebulib 
and neighbouring stars. The drawings are those of Sir John 
Herschel made in 1833 and 1837 with his 20-foot reflector of 
18^ inches aperture; of Lament (1837) with the 11 -inch Munich 
refractor; of Mason (1839) with a 14-foot reflector of 12 inches; 
of Lassell (1862) with his 4-foot reflector at Malta; Trouvelot 
{1875) with a 6i-inch Merz refractor; and Trouvelot and Holden 
jointly (1875), with the 26-inch refractor of the Naval Obserra- 
tory at Washington. 

To examine the question as to the motion of the nebula 
relative to the stars, Professor Holden has divided the drawings 
into three groups, the^r^?^ consisting of those made before 1840 ; 
the second, of LasselTs beautiful delineation, to which a great 
weight is given ; and the ihird of the two drawings made in 
1875, ^"® ^^ Cambridge, U.S., and the other at Washington. 
To prove the existence of a change, he has considered it necessary 
and sufficient to show that there has been an alteration in the 
position of some prominent feature, such as the " horseshoe," 
in the interval between the epoch of the first group and the 
second ; and that this apparent change is con6rmed and oon- 

* Aiiurican Journal of Science and Arts, No. 65, xi., May 1876, 



Feb. 1877. Fi/ly'Seventh Anntud General Meeting, 203 

tinned in the two drawings of 1875, greater weight being given 
to that obtained with the larger instmment. Professor Hoiden 
remarks : '^ It must be remembered that with two instmments of 
ifiiai light y hardly more discrepancy in the positions of the brighter 

rions of the nebula is to be expected than in the star-positions, 
these positions are determined by the stars themselyes, and 
on be assigned with almost no error in a nebula which contains 
80 many stars as the one under consideration. The fainter 
portions may vary greatly from the smaller to the larger instru- 
nents.'* Tables are given by Mr. Hoiden containing a comparison 
of the relative positions of the stars as laid down in the different 
drawings, which, on the whole, fairly agree ; and in another table 
be has exhibited, in a convenient form, the evidence for or against 
auction of the "horseshoe," with reference to its contained stars. 
Ala final result of the comparison, he concludes that the tables 
^ dtow that the stars have remained in their relative positions from 
1837 to 1875, ^^^ ^^^^ ''the drawings, whether taken as a whole 
or considered according to their relative importance, show that 
^'horseshoe ' has moved with reference to the stars, while the 
^onanan streak has not moved ; and that, therefore, we have 
fences of a change going on in this nebula. This may be 
> Tentable change in the structure of the nebala itself, such 
•8 was suspected by Schroeter, confirmed by O. Strove, and 
■gJun confirmed by myself in the nebula of Orion ; or it may bo 
tbe bodily shifting of the whole nebula in space, in some plane 
incKned to the line of sight." 

Comparisons of other well-defined nebulae, on a similar plan 
fe Aat adopted by Mr. Hoiden, would probably give us much in- 
ronnation respecting the proper motions of different portions of 
'^bnlc. The diffienlty of making accurate delineations of such 
wlicate objects must, however, make us cautious in accepting 
^ apparent changes in the position of nebulae in relation to 
^ighbonring stars, unless they are confirmed by drawings of 
more than one observer at the beginning and end of each interval 
of time. 

As bearing on this subject, it may be mentioned that a well- 
ttecnted drawing of the neliula in Orhn, reduced from a larger 
delineation, has been presented to the Society by Signor Tempel, 
^ the Areetri Observatory, near Florence. It is a valuable 
edition to the other representations of the same nebula already 
^ the possession of this Society. 



MatUigny^s Researches on Sciniillatwn, 

The Council have already noticed in a previous report the im- 
portant researches of M. M(miigny on the scintillation of the stars. 
*D a paper contained in the ** Bulletins dc VAcadcmie lioyale de 



204 Beport of tJte Council to tits XlXYlI. 4, 

Belgiqjie** (2me s^rie, t. xlii., No. 8, AoM 1876), M. Montigny 
has given an abstract of the resnlts recently obtained by him 
from some fnrther investigations on the same subject, espeoiallj 
in relation to the connection of the intensity of the scintUIatioiiB 
with the variations in the conditions of atmospheric phenomena. 
This very interesting astro-meteorological question has occnpied 
the attention of M. Montigny for several years past, the obser- 
vations discussed in the present paper extending from October 
1870 to August 1876. They were continued, with occasioiial 
interruptions, during this interval as ofben as the state of Uie 
weather permitted, and under the influence of varying conditions 
of the atmosphere, and of a different temperature, which in 
December 1870 and January 187 1 and 1876 was as low as — 9* 
and — 10° centigi*ade. 

The instrument employed was an astronomical telescope of 77 
millimetres aperture, with a magnifying power of 85. A scin- 
tillometer, formed of a circular plate of thick glass, was moonted 
obliquely in the tube of the telescope, in front of the eye-pieoe, 
and having a circular motion by means of a contrivance placed 
outside the telescope, by which the exact number of revolatioiif 
which the plate makes in a second of time can be ascertained. B] 
this arrangement the image of any star towards which the teL» 
scope may be directed describes a perfect circumference in thf 
field of the instrument. When there is no scintillation, the cirok 
forms a continuous line presenting the general tint of the star 
but when it is visible, this circular curve is broken into colonrei 
arcs, varying rapidly, among which may ordinarily be detecte* 
red, orange, yellow, green, blue, and occasionally violet, accordin. 
to the character of the scintillation. By means of a micrometea 
wire placed in the focus of the telescope, the number of colonre 
arcs contained in the curve described by the stellar image 
obtained and the amount of intensity determined. About sevenV 
stars were selected for the experiments, varying from the first 
the fourth magnitudes, and they are included in the three pri 
cipal types, according to Padre Secchi's classification. The stak 
observed on each evening were those situated in the eastern a^ 
western portions of the heavens, and owing to the continuity 
the observations this method of selection had the effect ^ 
obtaining results for each star, when situated in opposite quart&J 
of the sky, at intervals of several months. 

M. Montigny gives a series of tables of comparison betweei 
the intensities of scintillation and different meteorologirical cata, 
determined from observations made at the Observatory of Bms- 
tsels. The tables exhibit the intensities ranged in order of the 
seasons, of single rainy days, of consecutive miny days, of days ol 
high wind and storms, etc., leaving a comparison of other data it 
relation to the temperature of the air, atmospheric pressure, anc 
some other phenomena, for another paper. Important resulti 
are shown in these comparison tables ; among them it may bi 
noticed thai in some seasons it was found that the intensity o 



Feb. 1877. Fifty'Seveiith Annual General Meeting, 205 

BciDtillation is decidedly grater in rainy than in dry weather, 
and more marked in winter than in summer, abont equal in spring 
and aatumn in dry weather, bat in general wet seasons the 
intensitj is greater in spring than in autumn. On stormy nights 
the scyitillation increases or diminishes in intensity with the rise 
and fall of the barometer, being greatest on the approach of a 
itorm, and again diminishing as it passes away. Other facts have 
been satisfactorily brought out, bat these are sufficient to show 
that most interesting results have been obtained by M. Montigny 
from bis systematic series of observations. 



Progress of Meteoric Astronomy during ths year 1876. 

The records of meteoric phenomena during the past year 
ooDprise a few falls of aerolites, the occasional appearances of 
wreral considerable fireballs, and a few obnervations relating to 
periodical star showers, and to radiant points of meteor showers 
oecnrring with less intensity on ordinary nights of the year. 

Of meteorites whose fall was witnessed, and specimens of 
which have been preserved, the following brief list supplies the 
kcilities and dates, and some of the particular characters of 
the aeroKtic falls :— 

Btta. Local M.T. Locality, and Bomarks. 

^^TSi Sept. 14 4^ p.m. Supino, Circ. Frwinone, Italy (Stone fall). 

^87^ April 20 3^ 40" p.m. Rowton, near Wellington, Salop, England 

(Iron-fall, 7} lbs.). 

^7^ June 28 11^-12^ a.m. Stalldalen, Dalecarlia, Sweden. Three or four 

stones fell — the largest 4J lbs. 

Aerolitic falls of less importance, or of which the occurrences 
*re less authentically reported, have also taken place on the 
Miowring dates : — 

Dite. Local M.T. Locality, and Remarks. 

•076, June 25 9^-10* a.ra. Kansas City, Missouri, U.S.A. No meteor 

seen ; but a small stone, weighing a few 
ounces, fell — too hot to be touched imme- 
diately — on the tin roof of a house, whirh 
it almost penetrate<l, and bounded off.* 

^^76, July 8 4^ a.m. Lrmisville, Kentucky. A stone fell, accom- 

panied by a report, in the streets of the 
tr)wn, weighing about 2lbs.t 

^fivr. Joitm. 0/ Science, vol. xii., p. 316 : October 1876. 
^ Loui»mU^ Courier JournaJ {S<^ientific Amftican, of Aug. 12. 1876. p. 98). 
« large meteor {jnee below, p. 21 1) wa«< seen on the >;in»e date in Imliiina. 



2o6 Report of the Council to the XTXVil. ^ 

Date. Local M.T. Locality, and Remarks. 

1876, Oct. 19 2^ a.m. Newburyport (Mass.) and Ledyard (C011.1 

U.S.A. A large fireball seen at the 
place; and numerous meteoric stones 
found at the latter place on the daj^ foILoir^ 
ing its appearance.* 

Among these meteorites, the Bowton aerosiderite is partica' 
larly interesting, as it is only the seventh example of a solid 11 
meteorite whose descent has been witnessed, and of which 
specimen has been preserved. It fell in rainy weather, onac- -*" 
companied by any visible fireball, but preceded by two startling***^ 
detonations heard northward from the Wrekin over the neigh- - 
bonring villages of Shropshire for many miles. It penetrated - 
the soil of a turf- field to a depth of eighteen inches, almost verti- ^ 
cally, but with a slight inclination (from the north-west towarda^i 
south-east), and when discovered abont an hour after the occur- 
rence it was still quite warm. It was presented to the Britiahjfl 
Museum by his Ghnace the Duke of Cleveland, in whose property^ 
it fell ; and a cast of the meteorite may be compared wiU^ 
similar casts of the iron meteorites of Braunau, Victoria Wes^^ 
(S. Africa), Nidigullam (Madras), Marysville, and CharlottiMii 
(Dickson Co.), U.S.A., of which, with that of Agram, isB: 
Croatia, the actual falls have previously been witnessed. Th'L.d 
meteorite itself is undergoing section and preparation for a=- 
analytical examination of its composition. The stone-fall mt£ 
Supino, in Italy, on September 14, 1875, happened on thaK 
same day as the appearance of the large detonating fireball i-.:^ 
England described in last year's Report (Mo7ithly Notice^ "^ 
vol. xxxvi., p. 216), and the coincidence appears to be parti- 
cularly deserving of attention, as it was stated in the Brad/or"^ 
Times (Nature, September 23, 1875), that the detonation whica^ 
followed the meteor's appearance at that place was so lou— 
as to be plainly heard indoors by those who had not seen tl^^ 
meteor, which more clearly established its aerolitic charact^^- 
than had been suspected in last year's Report. The coincidence^ 
of a stone-fall on the same date, if not purely accidental, rais^^ 
a reasonable conjecture that it may have belonged (with the ■ 
aerolitic fireball simultaneously observed) to a shower of ordinary 
shooting stars whose approximately known itidiant point wiw 
found to agree exactly with the true course or direction of flight 
of the detonating meteor ; for it will be remembered that a com- 
parison of many well- accordant descriptions of its apparent path 
extensively observed in Enp:land enabled the true direction and 
the real path of the large fireball of September 14, 1875, tobe 
determined with more than ordinary certainty and precision. 

♦ New York Observer, Thiirsdav. Nov. 9. 1876. Tho asserted fall of a 
small stone, apparently meteorir, statod in Nature, vol. xv., p. 305, to have 
been observed at EccUsfechan, near Gbifig^ow, on the evening of Jan. 2, 1877, 
may be added to the above list of Hupposed falls of aerolites recently recorded. 



Feb. 1877. Fifty-seventh Annual OeneraJ Meeting, 207 

The fireballs of lar^ size which have been recorded daring the 
past year may be briefly noticed here under three separate de- 
Bcriptions. Among the first, or detonating class, the following 
ippear to have been the most conspicnons examples : — 

SkM. WMh. M.T. Locality, and Ramarks. 

1875. Dec. 27 9^-9^ 20* p.m. Kansas, Missouri, atid Iowa States, U.S. A 

large firc1»all bursting into many frag- 
ments, and leaving a laminous smoke- 
track, vij*ible for 15", commenced its 
course over Nebraska, 120 miles west 
of Missouri K., and ex|)l(>dt><U with heavy 
detonations, over Missouri State. Real 
motion due eastward, with a steep in- 
clination towards the Earth. 

187^ Jan. 5 10^ 30" p.m. Iowa and Missouri, U.S. A large and bril- 

liant fireball, ezpbjding with many 
thunder-like rep<.)rt8. Its true oonrNo 
was nearly vertically downwards fr«»m 
north-west towards south-east. 

1876, Jan. 31 5^ 30P p.m. Louisville, Kentucky, and Tennessee, U.S. 

A large fireball observwl by I>r. Lawrence 
Smith; said by some olfservers to have 
been followed by sounds of an explonitm. 

Local M.T. 
1876, June 15 8^ lo" p.m. Suez to Port Snid. A largo fireball, which 

burst with a very loud explosion, illu- 
minating the 8ky brightly at all the 
stations on the Maritime Canal ; m(»\'iTig 
from went to east, or from south to north. 
Vertically over the Deversoir, and li^aviiiu^ 
a light streak there at the point when- it, 
exploited. 

A large fireball which was perhaps also detonatinpf (see below, 
P'2ii) was observed in France at about 9** p.m., on November 5, 
^'76. In the second class of fireballs may be included those 
^kich have been sufficiently observed in England to afford 
•"^uis of determining, at least approximately, the real height 
*^ position of their tracks, and the real direction or apparent 
*?diaiit.point from which they took their flight. The following 
•^comprises all the comparisons of thi.s kind which have been 
opined from the best available descriptions, and it relates in 
gCBeral to those fireballs which have been most genenilly 
observed in England during the past year : — 



2o8 



Bepoii of the Council to the 



XZXTIL 




^•5 8 



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^ ^ I ^- 






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>8^s 



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F^.semUh AnrmH Oeneral Meetmg. 



209 



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Feb. 1877. F^hf-sevenih AnwucU Oeneral Meeting, 911 

In addition to the above accordant observations, simnlianeoiiB 
records of 15 or 20 bright meteors and shooting stars, chiefly 
between Mr. W. F. Denning's station at Bristol, and the Bad- 
diffe Observatory, Oxford, have been obtained, of which the 
pirticiiiars will afford available materials for calcnlation. The 
timeB of appearance and general description of other consider- 
ible meteors during the past year, as far as accounts of them 
kve been received, appear to have been as follows : — 

IMe. 
1(76, Feb. 4 7^ 35" p.m. Nucleus with fi^lobular disk several minutes 

in diameter; seen moving slowly west- 
wards, in the south, at Bristol. 
FariiTIme. 
i^iXtf. 19 11^ 13" pjn. Fireball recorded by M. Ghapelas Conlyier 

(^ravier, at the Observatory of the Luxem- 
bourg, in Paris. 

1876, April 15 8^ 33" p.m. Meteor with a bright disk; seen in the 

western twilight at Bristol, and at Hawk- 
hurst (Kent). 
WMih. X.T. 

lo?^ July 8 S^ 45" p.m. Indianopolis, and Indiana State. U.S. A 

fireball of the largest class; half the 
appar. diam. of the Moon, leaving a streak 
of light for 40^ ; no detonation heard. 
Traversed an arc of 30° north-westwarda 
from Cassiopeia. 

1896, Aug. 31 gh iQP p.m. Bolide with large elongated nucleus. Man- 

chester ; and at London and Sheemess. 
(Fell in the north.) 

1% Aug. 22 8* 40" p.m. At Scarborough ; very bright. Fell in the 

E.S.E. nearly to the sea, from alt. about 

60^ in the S.E. 
j^ Paris Time. 

I076. For. 5 gk 40^-9** p.m. Largo fireball. Departments of Mame and 

Aube, France; a detonation is said to 

have been heard in the latter district at 

Clery. At Choisi-le-Boy the meteor's 

course was from a Aurigm to a Ursts 

Majoris, and along this line it left a 

momentary streak. The meteor's course 

is direct^ from Tawrus and Auriga. 

1876, Nov. 6 f 45» p.m. A large fireball at Orsay, Paris, moving 

slowly at a low altitude in the E.N.E. 
southwards. Bright, but smaller than the 
Moon's disk, leaving a slight streak on its 
course. Very probably a ** Taurid " seen 
with slow foreshortened course near its 
railiant point. 

Q 2 



aia Eeport of the OouncU to the xxxvn. 4, 

1876, Nov. 6 Between 8*'-9^ p.m. A large meteor seen in Kent, Herts, and 

Lancashire, descending almost verticaUj 
in N. and E. (Kent and Herts), and in the 
West (Lancashire*); (?) two meteozs. 
Divided into two parts, or disappeared 
with two separate explosions. Not 
directed from Taurus, 

1876, Nov. 7 7* 19" p.m. Fireball in CaprieomuB ; Writtle (Essok). 

Burst with a bright flash 6° under /9 Capr, 
Path 10° in 3 seconds, directed from jSs- 
turn. Very probably a distant " Tanrid." 

1876, Dec. 13 4*" 45" p.m. A bright fireball, in daylight, when veiy 

few stars were yet visible ; seen from nesf 
London, Famborough (Hants), &c. ; in the 
N.E. descending from west to east with a 
course of some length to near the B, 
horizon. Yellow, bluish green, and red at 
last, with a trail of sparks, which re- 
mained visible for a few moments. The 
descriptions of this fireball's course cor- 
respond very nearly with that of the 
daylight meteor of December 22, 1875, 
at I** 40°* p.m., described in the last 
volume of these Notices ; * and it appertains 
not improbably to a meteor-system of the 
same group, with a radiant-point near 
/3 HerctUis. 

Of the real courses of the many bright meteors here described 
veiy little is accnrately known, and it is much to be desired that 
in describing apparitions of such remarkable phenomena observers 
would endeavour to ascertain correctly and express clearly the 
apparent positions in the sky of the tracks along which these 
celestial intruders upon the Earth in its motion round the Son 
pass across their field of view. 

The periodical star showers of the past year have been either 
inconspicuous or much concealed by cloudy weather, and 
scarcely any notes of them of very remarkable importance were 
obtained. A meteor shower of some intensity was observed 
on the night of the i8th of April 1876, at Bloomington, 
Indiana, U.S., of which the appearance was recorded, and some 
particulars were gathered by Professor Kirk wood, of the State 
University of that town. The meteors were sufficiently nume- 
rous and bright to attract the attention of ordinary observers, 
and from their description the radiant point of the shower ap- 
pears to have been in the neighbourhood of the constellation 

• Vol. xxxvi., p. 217. — Erratum: line 19 firom bottom of the page, f^r 
Brangling, read Braughing. 



M. 1877. lyty^Mvenih Annwd General Meeting. 313 

Ljfra, As the year was a leap-year the expected time of ap- 
pearance of the shower would be on the i8th instead of on the 
i9th-2oth of April as it returns in ordinary years. Another 
meteor shower of greater brilliancy was observed on the night of 
October 18, 1876; and its appearance was similarly recorded 
bj Professor Kirkwood from the concurrent testimonies of 
numeroas observers of the many bright meteors which were 
TJsible at Bloomington on that night. The radiant-point was in 
Amga or between Taurus and AiMriga, and it may not impossibly 
bave been distinct from the usual maximum recurrence of the 
well-marked shower from Orion on that date. From the narra- 
tne (above quoted) of the appearance of a large meteor (perhaps 
aaobtic) early on the following morning in Massachusetts, it 
nij also be added that frequent small shooting stars were still 
we there at 2^ a.m. on October 19, and it is said that two 
or three of the shooting stars seen at Bloomington between 
9* 45" and 11^ 15™ p.m. on the i8th were noticed to be exceed- 
nigij conspicuous by their size and brightness. Of these and 
o^er star showers, with the exception of that of August last, 
no observations were obtained in England. The sky was clear 
dnring the period of the August shower, but the Moon had 
Karoely passed its full, and was unfavourable to observations 
^ the later hours. The maximum of the shower occurred on 
^ night of the loth, and it was so unimportant in intensity 
^sompared with many previous displays that one observer watohing 
&(teff sky could at the most only count about 25 or 30 Perseids 
P^boor together with 10 or 12 sporadic shooting stars, while the 
bombers seen on the nights of the 9th and nth were much less 
tiJMi tbis. Even allowing for the effect of the Moon's light in 
extinguishing the smallest meteors of the Ferseid shower, the 
observations all indicated very clearly a distinctly marked dimi- 
Jmtion in the intensity of the August showers in 1876 as com- 
pared with ite brightness in 1875, and in several of the imme- 
«8tely preceding years. Among the records of the shower in 
"^land are several simultaneous observations, two of them of 
bright Pers&ids (on August 1 1 and 1 3) and one of an Aquilid 
or A(iuariad on the 15th, of which only a few calculations 
(those above described) have yet been brought to a conclusion. 
p6 radiant point of the shower was accurate, in spite of 
ri« fiuntness, near j; Fersei-^ but the presence of another 
'^diant point in Oasdopeia was also recognised on certain nights 
ot the shower as exhibiting simultaneously with it a very 
^narked activity, which scarcely, however, permitted its position 
to be very accurately determined. Watches were maintained 
^thont success at well-equipped stations and under favourable 
cations of the sky for the Leonids and Andromedes of 
November 1876. At Clermond Ferrand, in France, Mr. Gruey, 
^s'Jstedby one companion during a part of the watch, saw only 
five meteors on the first and even fewer falling stars on the 
Kcond morning during intervals of four hoars' duration, each 



314 Report of the OouncU to the xxxnr. 4, 

after midnight a.in. of November 13 and 14, althongh the 
sky was clear. During the honr from 2^ 30** to 3^ 38™ Ott 
the morning of November 15, when the sky was veiy oleftr, 
only one meteor was observed. None of these shooting stars 
appear to have been conformable to the radiant point in 
Leo. The observations of the same shower in 1875, indading 
those communicated last year to the Astronomical Society 
by the Astronomer-Boyal,* clearly indicate that the November 
shower has ceased to be conspicuous on the accustomed datee ; 
but a progressive tendency of the shower to reach its maximum 
on the morning of the 15th instead of the 14th of November, ob- 
servable in the years ending with November 15, 187a, is notdoe- 
able in all more recent observations of the Leonids, and may have 
continued to retard its date, unperceived by observers on the 
ordinary nights of observation, since that time. Three small 
Leonids, leaving white streaks for two or three seconds, seen near 
the radiant point in Leo by Mr. Denning, at Bristol, on the morn- 
ing of November 19 (with two others on the following morning), 
diverging accurately from a point at R.A. 149**, Decl. +22** j, 
together with the absence of any such indications of the shower 
in France on the mornings of the 13th- 15th of November last, may 
perhaps be accounted for by a considerable deformation of the 
meteor stream, and a consequent sensible change of position of 
its nodal points, in the portions forming the terminal or rotreating^ 
phases of the shower. 

No indications of the Andromedes were observed by Mr. 
Denning on later mornings of November, and a watch for them 
kept at other stations on the last few evenings of the month, 
when the sky was clear, was also without success. The shower 
of the " Oeminids " of December 12 appears to have furnished a 
large proportion of shooting stars as early as December 8 and 
9 ; but cloudy skies on the following nights prevented the time 
of its maximum from being ascertconed. No observations on 
the periodic shower-date of January 1-3, 1877, have yet been 
received, and it is to be feared that the unfavourable conditions 
of the full Moon and cloudy weather have again provented this 
rarely distinguishable star shower from being satisfsictorily ob- 
served. 

The observations of shooting stars at the Badcliffe Observa- 
tory, Oxford (included in the publications of that Observatory for 
the year 1874), continued to be recorded with accuracy and ampli- 
tude during the past year ; and fifteen of the meteors registered 
aro identifiable with meteors of various magnitudes which have 

* Monthly NoiiceSf vol. zxzvi., p. 272, March 1876. 

t For easy representation of the lengths of paths, altitudes, and anmntha 
of meteors, etc., in degrees, it is found convenient to employ this mode of 
reckoning RA. instead of the usual method of expressing it in time, and to 
describe declinations north or south of the Equator with a -(- or — sign, as a 
brief way of recording the apparent paths, and hence also most conveniently in 
cbait« of this description, the positions of ^he radiant points of ahooting stars. 



i877- FiftyseverM Anfwai OenerdL Meeting, 



"5 



been elsewhare obflerved, and whose real paths it will be possible 
to compute with some precisioii. The Laminoos Meteor Gom- 
mittee of the British Association has resumed its examination of 
these and of other meteor tracks communicated to it by observers, 
with a view to presenting in the most convenient form for their 
coDstant reference a table and map of the centres or regions of 
dirergenoe of shooting stars on ordinary nights of the year, at 
pneent known with the greatest certainty to exist ; and a key- 
Dip and table, constmcted for this purpose by Mr. Greg, were 
praKated, with the Beport of the Committee, to the British Asso- 
dition in September last, as the first completed stage in the 
pogress of their undertaking. It is also intended to embody the 
owoffiie and map with the original lists of meteor showers by 
nfiridiial observers from which it is constructed, in a suitable 
tat or pamphlet, with instructions for recording, and directions 
of the days most desirable for registering shooting stars, to serve 
(tanen as a useful ephemeris to guide them in their observa- 
fini; and this design the Committee hopes during the coming 
JMr to be able to cany out. 



tf 






2i6 xxxvn. 4 



Report of the Audiiora. 

The following Report of the Auditors was presented to tin 
meeting at the conclnsion of the reading of the Report of tb 
Council, in conformity with bye-law No. 65. The balance-shee 
of the Auditors, however, differs in arrangement in some mine 
particulars from that of the Treasurer, presented to the Cound 
and printed in their Report, but the bsJances in hand as states 
in the two balance-sheets are precisely the same. — [e. d.] 

" We, the undersigned, being the Auditors appointed, at tb 
meeting of this Society held on the 12th of January last, t 
examine the accounts of the Society, in pursaance of the 65! 
bye-law, for the year ending 31st of December 1876, do repoi 
as follows : — 

'' I. The paper writing hereto annexed and marked A, an 
verified with our signatures, contains a true and correct stab 
ment of the receipts and expenditure of the Treasurer, 
account of the Society, firom the ist of January to the 3i8t < 
December 1876, inclusive. 

" The available balances in the hands of the Bankers and tb 
Secretary of the Library Committee amounted to the sum. ( 
£270. is«. $d, 

" 2. The paper writing hereto annexed and marked B, an 
also verified with our signatures, contains a true statement of tli 
funded property of the Society on the same day, as far as we ai 
able to ascertain it. 

" 3. We have examined, as far as circumstances would permi 
the state of the rest of the property of the Society, consisting < 

" Instruments ; 
t " Books in the Library ; 

" Stock of the Society's Publications. 

" With regard to the instruments, we have to report thi 
some of them, viz. Nos. 11, 21, 32, 64, 66, 68, 71, 73,* and ; 
in the list contained in the Report of the Council in 1876, a: 
missing. The remainder, including Nos. 28 and 49 in the san 
list, which have been found since that report, are, with fr 
exceptions, in good order and preservation. We have 
thought it necessary to enter into minute particulars on \ 
subject, as a very careful examination of them was made ] 
viously to the last general meeting by Mr. Lecky, the principal { 

* No. 73 has been removed from the list of the Society's instrument 
9rder of the Council.— [b. d.] 



M1877. BtfcH cf Ob AvMan. 817 

of whose veport was inserted in ihe McmtKhf NoUees of Febroazy 
kit 

'^ As no onUogoe of the books in ihe Hbruy has bee^ 
m are nnable to say whether they sro oorrect in point of 
somber. We stmngly advise, in Hie general interest of the 
Sodetyy that a catalogue should be made as soon as possible. 

"We have had the same diffionlly in dealing with the stock of 
fte Sodetr's pnbHcations as was mentioned 1^ the Anditors of 
htiyeary tibongh not by any means to the same extent. It is, 
ttd ihraTB wul be, ezoeedingly difficult to check the issue of 
■fifidnal copies of each of ue Memoirs and Monthly NoHeea^ 
htfliey ai« now in a very much better state than at the last 
wHL The perfect Tolnmee have been carefully packed in 
Modi, witii the number of copies contained marked on each. 
«• We not examined the wh^ but have opened some half- 
fan, adeeted by chance, and have in every instance found the 
nakier to correspond with the labeL 

'' Fbakoib Baebow. 
'' Abtuub Bbiwih. 
''J. ELiNinDy Esdaile. 

«NMy8,i877." 



ai8 



Report of the Auditors. 



RECEIPTS. 

Balance at Bankers', Dec. 31, 1875 

in hand of Secretary of libiury Committee : 
on account of Library Expenses 
„ Tumor Fund 

in hand on Petty Cash Account 



ff 



}» 



tt 



If 



Dividend on £3,700 Consols 

j£5,200 New 3 per Cents. ... 

£4,000 Consols 

„ £5,200 New 3 per Cents. ... 

Received on account of Subscriptions : 

Arrears of Contributions 

237 Contributions for 1876 

On accdunt of do 

28 Admission Fees 

20 First Contributions 

1 1 Composition Fees 

Sale of Publications at Society's rooms ... 

„ at Williams & Norgate's 

Balance of Horroz Memorial Fund 

Bequest of the late T. C. Janson, Esq., to the 

Lee Fund 
Due to Assistant Secretary, Dec. 31, 1876, 

Petty Cash Account 

Due on outstanding cheque 



on 



£ 8, 


d 


£ 


548 18 


9 




32 3 







21 







13 4 


II 


61S 


55 


9 


77 7 







59 5 
77 



6 


268 


106 I 





497 14 







2 







60 18 







32 " 





699 






52 18 


8 


231 


23 I 





75 
38 







aoo 

2 
IS 



£2,146 



'©!>. 1^7- 



Sepcri of the AudUan. 



919 



EXPENDITXJRE. 

Editor of MotUhly Notices (five quarters) .. 
Assistant Secretary (five quarters) .. 

icome Tax and House Duty 

Insurance ... ... ... .. 

Lting:— 

SpotUswoode & Oo 

Hazell, Watson, & Vinej 

Holdgate Bros, (printing plates) .. 

atlaographj, Engraying, &c. : — 

Chatham School of Photography .. 
W. H, Wesley ... .*• .. 



^^kg and Stitching: J. Bomfitt 
^l^iJuy expenses, binding books, &c. .. 
'^^^not Fund : Books purchased during year .. 

^**flilaneou8 : — 

•Qonse expenses ... .*. ... 

'v OjKvB ••■ ••• ••• ••• •■ 

Stamps and postage ... ... ... .. 

Oarriage of books and parcels 

Stationery and office expenses 

^Blxpenses of meetings 

Ooals and gas 

^ftCrs. Jackson-Ghrilt's annuity 

Sittings in Library &c. : Whitechurch Bros 
Sundries ... 
Ifiankers' commission &c. 
^ew Cheque-book 



^^«tments : — 

Purchase of £300 Consols, at 96f , including 
Commission ... ... 

Turchase of £200 Consols, at 95f , including 
Commission 

^^^Jice at Bankers', Dec 31, 1876 

In hand of Secretary of Library Committee : 

On account of Library expenses 

„ Tumor Fund 



£ 8. d. 

75 o o 

187 10 o 



364 8 o 

187 12 o 

18 5 o 



5 10 o 
51 2 o 



28 7 7 
23 17 o 
49 10 8 
882 
860 
17 15 6 

74 19 9 
8 19 o 

5 14 6 

20 19 8 

006 

084 



289 10 o 



191 10 o 

253 I lO 

13 8 6 
22 3 9 



A. 



£ $, d. 



262 10 o 

5 5 o 
7 16 6 



570 5 o 



56 12 o 

39 17 3 

138 14 6 

48 16 3 



247 6 8 



481 o o 



288 14 I 

£2,146 l^ 3 



Fbancis Babbow. 
Abthtjr Bbewin. 
J. Kemickdy EsDAn.K. 



220 Report of the Auditors, xxxv 



B. 



Assets and present Property of the Society, Jannar 
1877: — 



Balance at Bankers*, Dec. 31, 1876 

Less amount of outstanding cheque 

Due on account of subscriptions : — 

2 contributions of 5 years' standing 
2 If 4 >« ••• 

n »» 3 »» ••• 

22 ,y 2 ,) .«. 

09 tt ^ »l ••• 

2 admission fees ... 

2 first contributions 

and one amount of 

Balance in hand : — 

In hand of Secretary of Library Committee : 
On account of Library expenses 
On account of Turnor Fund 



35 12 3 
Less amount due to Assistant Secretary 
on Petty Cash Account, Dec 31, 1876 2 18 8 



£ 


t. 


d. 


253 


I 


10 


15 








21 








16 


16 





69 


6 





92 


8 





144 


18 





4 


4 





2 


2 





5 


5 





13 


8 


6 


22 


3 


9 



£5,200 New 3 per Cents., including Mrs. Jackson-G wilt's Gift 

(^300). 
£6,200 Consols, including the Leo Fund (£300); the Tumor 

Fund (£450) ; the Ilorrox Memorial Fund (£ioo) ; and Mr. 

Carrington's bequest of £2,000 Stock which has been 

transferred to the Society during the past year. 

Unsold Publications of the Society, various astronomical instru- 
ments, books, prints, &c. 

Two Gold Medals in stock. 

Balance of Tumor Fund included in Treasurer's Account, 
£129. 5«. 6d. 



238 



355 



32 



FiiANas Babrow. 
Abthub Brewin. 
J. Kenxkdt £sdai 



Feb. 1877. 221 



Papers read before the Society from Fehrua/ry iSj 6 to 

Februwry 1877. 

1876. 
Mar. 10. The Stereo-Micrometer. Prof. Zenger. 

Occnltation of the Pleiades observed at Madras on 
Jan. 7, 1876. Mr. N. R. Pogson. 

Abstract of Prof. Christian Mayer's paper on the 
Observations of Binary Stars discovered at the 
Mannheim Observatory, Mr. S. M. Drach. 

On the proper Motions of the two components of the 
Binary system a Gentaun. Mr. E. Jt Stone. 

On a supposed Variability of the Proper Motion of 
B.A.C. 793. Mr. E. J. Stone. 

Micrometer-measures of SaiwrrCs satellites made at 
the Boyal Observatory, Greenwich, in the year 
1875. "^^^ Astronomer-Boyal. 

Comparisons of recent and former Observations of 
Bji.C. 793, and remarks on the alleged Variability 
of its proper Motion. Mr. Dunkin. 

Note on a Starlit Transit Eye-piece. Dr. Boyston 
Pigott. 

Obs^ations of the November Meteors made at the 
Boyal Observatory, Greenwich, in 1875. T^® 
Astronomer-Boyal. 

Preliminary Note on Photographing the least re- 
fracted portion of the Solar Spectrum. Capt. W. 
de W. Abney. 

Beferenoe Catalogue of Astronomical papers and 
Besearches. Mr. Knobel. 
12. On the most probable Result which can be derived 
from a number of direct Determinations with 
assigned Weights. Mr. E. J. Stone. 

A list of Stars beyond the ordinary limits of Distance, 
inserted as double in Sir John HerschePs General 
Catalogue of Double Stars. M. Flammarion. 

Badiant Points of Shooting Stars. Mr. W. F. 
Denning. 

Near approach of 47 Oeminorum. Bev. S. J. John- 
son. 

An Instrument for determining Spherical Triangles 
by Mechanical action. Mr. F. C. Penrose. 

Note on the two exterior Satellites of Uranus. Bev. 
T. W. Webb. 



92a Papers redd before the Society, ZZXVIL 4, 

May 12. On our Sidereal System, and fche Direction and Dis- 
tance to its Centre. Mr. J. Ennis. 

Note on the Conjunction of Verms and X Geminorvm 
on August 17-18, 1876. Mr. Dunkin. 

On recent American determinationB of Geographical 
positions in the West Indies and Central America. 
Major H. S. Palmer. 

A Catalogue of red double Stars. Mr. S. W. Bum- 
ham. 

Observations of Minor Planets made at the Observa- 
tory of Marseilles. M. E. Stephan. 

Note on the Discovery and Observations of Minor 
Planets (»^) to (^^3), Mr. Dunkin. 

Note on Coggia's Comet (DX 1874). Mr. J; 
Dreyer. 

On the relative Power of Achromatic and Beflecting 
Telescopes. Dr. T. B. Bobinson* 

Note on the Satellites of UranttsJ^^^Mr. E. Neison. 

Note on Dr. Boyston Pigott's S^lit Transit Eye- 
piece. Capt. W. Noble. 

Visibility of Oberon and Titama, Mr. Bogerson. 

On Loh^mann's and Schmidt's Lunar Maps, and 
Note on a new red Star. Mr. J. Birmingham. 

Spectroscopic results for the Motions of Stars in the 
line of sight made at the Boyal Observatory, 
Greenwich. The Astronomer-Boy al. 

Note on the Displacement of Lines in the Spectra of 
Stars. Mr. W. H. M. Christie. 

On Precession. Dr. Berg. 

On the Transit across the Sun's disk of the second, or 
great Comet of 1 819. Mr. J. B. Hind. 
June 9. On the Atmosphere of Venus. Mr. E. Neison. 

Bemarks in connection with his five volumes of 
Solar drawings. Bev. F. Hewlett. 

On the Determination of the Distances of a Comet 
from the Earth from three Observations. Dr. 
Berg. 

Visibility of Mercury and Venus in sunshine. Mr. 
W. F. Denning. 

Elements of Minor Planets (»^0> ('^*) a^^ ('^^)« 

Mr. Dunkin. 
On a hitherto unnoticed apparent inequality in the 

Longitude of the Moon. Prof. S. Newcomb. 
Photometric experiments upon the Light of Venus. 

Mr. J. I. Plnmmer. 
Observations of Venus. Capt. W. Noble. 
On the proper Motion of the bright Spots on Jupit 

Mr. J. Brett. 
Note on a method of obtaining Equatoreal Motion 

an Altazimuth Stand. Lord Lindsay. 
Note on a Double Lnage Spectroscope. Lord Lindas 



•"^^ X877. Papers read hefore the Society, 323 

^^- 10. Measarement of the direct Effects of Sun-spots on 
Terrestrial Climates. Prof. Langley. 

Observations of Planets with the Transit Circle at 
Dnblin (Dnnsink). Dr. B. Copeland. 

Obflervations of Lnnar Eclipse of 1876, September 3, 
made at Cadiz. Senor A. T. Arcimis. 

A method of deducing the Formula for correcting 
the Computed Time of an observed Occultation 
for errors in the Elements adopted. Mr. W. H. 
Finlay. 
T)e8cripftion of an Improved Altazimuth Stand for 
Befleoting Telescopes, with a new form of Binocular 
Eye-piece. Mr. W. H. Thomthwaite. 
Spectroscopic observations of the Motions of Stars 
and of VeMw in the line of sight, and of the rota- 
tion of the Sun and of Jupiter, made at the Boyal 
Observatory, Greenwich. The Astronomer-Boyal. 
On the effect of wear in the Micrometer Screws of the 
Ghneenwioh Transit Circle. Mr. W. H. M. Christie. 
Observations of the Solar Eclipse of 1876, Sept. 17. 

Mr. J. Tebbutt. 
An endeavour to simplify the method of making the 
correction for the Spheroidal figure of the Earth in 
Lnnar observations, and particularly with reference 
to its effects upon the Lunar Distance. Mr. F. C. 
Penrose. 
3. A List of Binary and other interesting Double Stars. 

Messrs. J. M Wilson and J. Gledhill. 

On some phenomena of the Internal Contacts common 
to the Transits of Ventis, observed in 1769 and 
1874, and some remarks thereon. Mr. E. J. Stone. 

On some difiraction Experiments of M. Ch. Andr6, 
with reference to Astronomical Instruments, and 
the general theory of this Diffraction. Bev. S. J. 
Perry. 

On the Phenomena exhibited by a Planet in its 
transit across the Solar disk, from observations by 
M. Ch. Andre. Bev. S. J. Perry. 

Note oil the relative Space-penetrating power of the 
Pulkowa 15-inch Befractor, and Mr. Lassell's 4- foot 
Beflector. M. 0. Struve. 

On an Oversight in the " M^canique Celeste," and 
on th6 Internal Densities of the Planets. Mr. G. H. 
Darwin. 

On the Error of the tabular place of Verms on 
December 8, 1874. Col. Tennant. 

Note on the Gradation of Light on the disk of Ventis, 
Mr. W. H. M. Christie. 

On the Position of the point of maximum brightness 
on Venus, Mr. E. Neison. 



224 Papers read before the Society, xxxvn 

Note on Professor Langley's paper on the Dii 
Effects of Snn-spots on Terrestrial Climates. '. 
W. Mattieu Williams. 

1877. 
Jan. 12. On the Orbit of a Centomri, Mr. A. Marth. 

On the Conjunction of Verms and X C^emmorwm. 

J. I. Plnmmer. 
Theory of the Horizontal Photoheliograph, inclnd 

its application to the determination of the S 

Parallax by means of Transits of Vemta. F 

Harkness. 
On 0. M. MitchelPs Observations at Gincini 

Prof. Cleveland Abbe. 
Observations of Shooting Stars, April to Decem 

1876. Mr. W. F. Denning. 
Note on an Improved Mode of viewing the E 

Dr. W. Erck. 
Observations of Occnltations of Stars by the M( 

and phenomena of Jwpiter*s satellites, made at 

Boyal Observatory, Greenwich, in the year il 

The Astronomer- Royal. 
Micrometical Measures of Double Stars. Mr. 

Knott. 
'Ephemeris for determining the positions of 

satellites of Urcmus, Mr. A. Maribh. 
On the Orbit of a Oentcmri. Mr. J. B. Hind. 
The Specular Reflection hypothesis, and its beai 

on the Transits of Ven/us. Mr. J. Brett. 



Peb. 



J8fy. 225 



t of Pi^ ^E^Uc Institutions and of Persons who have contributed ttt 
the .jSocietifs Library 8fc, since the last Anniversary, 





Majesty's Government. 
Majesfy's Government in India. 
Majesty's Government in Australia. 
Lords Ck>mmi8sioners of tbe Admiralty. 
Government of Prussia. 
Government of the United States of America. 
Meteorological Office. 
Society of London, 
al Society of Edinburgh, 
al Greographical Society. 
al United Service Institution. 
Bo^^al Irish Academy. 
Ro,y al Dublin Society. 
Boj^al Asiatic Society of Great Britain. 
^K^y^al Asiatic Society of Bombay. 
Boy al Society of New South Wales. 
B^jral Society of Tasmania. 
-^*^^tic Society of Bengal. 

^l^ast Natural History and Philosophical Society 
^^^ish Association for the Advancement of Science. 
Bi'itiiah Horological Institute. 
Jf^^ncil of the City of Manchester, 
^^logical Society. 

I^ft^orary and Philosophical Society, Leeds, 
i^iterary and Philosophical Society, Liverpool. 
pj^.^t^ry and Philosophical Society, Manchester, 
r/^^losophical Society, Glasgow, 
p^^^orological Society, 
photographic Society. 
^*^ysical Society of London. 
^^gby School Natural History Society. 
^^^iety of Arts. 
"^logical Society of London. 
^^yal Observatory, Greenwich. 
^yal Observatory, Cape of Good Hope, 
^dcliffe Observatory, Oxford, 
"^^w Observatory, 
^mperial Observatory, Berlin. 
iDiperial Observatory, Vienna. 
National Observatory, Paris. 

B 



i 



2 26 List of Pvhlic Instituiimis 8fc. • xxx?u. 

Observatory, Cincinnati. 
' Observatory, Coimbra. 
Observatory, CoUegio Bomano. 
Observatory, Ley den. 
Observatory, Madrid. 
Observatory, Melbourne. 
Observatory, Milan. 
Observatory, Moncalieri. 
Observatory, Munich. 
Observatory, Prague. 
Observatory, Strasburg. 
Observatory, Sydney. 

United States Naval Observatory, Washington. 
Imperial Academy of Sciences, Berlin. 
Imperial Academy of Sciences, St. Petersburg. 
Imperial Academy of Sciences, Vienna. 
Royal Academy of Sciences, Brussels. 
Academy of Sciences, Paris. 
Academy of Sciences, Amsterdam. 
Academy of Sciences, Bologna. 
Academy of Sciences, Buda-Pesth. 
Academy of Sciences, Copenhagen. 
Academy of Sciences, Gottingen. 
Academy of Sciences, Montpellier. 
Academy of Sciences, Munich. 
Academy of Sciences, Stockholm. 
Academy of Sciences, Turin, 
Italian Society of Sciences, Rome. 
Pontifical Academy de Lincei. 
Society of Sciences, Batavia. 
Society of Sciences, Bordeaux. 
Society of Sciences, Cherbourg. 
Society of Sciences, Helsingfors. 
Society of Sciences, Leipsig. 
Society of Sciences, Zurich. 
Mathematical Society of France. 
Museo Fisico, Florence. 
Mus^e Teyler, Leyden. 
Bureau des Longitudes. 
Depot General de la Marine. 
Imperial University of Kasan. 
Italian Spectroscopic Society. 
Astronomische Gesellschaft, Leipsig. 
Berlin Physical Society. 

International Committee of Weights and Measures, 
Smithsonian Institution, Washington. 
American Academy of Sciences. 
American Philosophical Society. 
American Bureau of Navigation. 
Franklin Institute, Philadelphia. 



fc xfi77. 



List of PMic In$Hiuti(m8 8fc. 



227 



Canadian Institate. 

Connecticat Academy. 

Orleans County Society. 

Toronto Meteorological Office. 

Editor of the AthensBam. 

Editors of the American Jonmal of Science and Arts. 

Editor of the Astronomical Register. • 

Editor of Bulletin des Sciences Math^matiqnes, &c. 

Editor of the English Mechanic. 

Editor of the Natnrforscher. 

Editors of the Philosophical Magazine. 

Editor of the Quarterly Journal of Science. 

Editor of the Revue Scientifique. 

Editor of Sinus. 

Editor of the Telegraphic Journal. 



. Abbatt, Esq. 
. A. Abetti. 
apt. W. de W. Abney. 
enor A. T. Arcimis. 
rof . J. J. Astrand. 
. S. Baden-Powell, Esq. 
V. H. R. Bailey. 
. Bird, Esq., Executors of. 
. R. Birt, Esq. 
. Bonomi, Esq. 
. W. Bosanquet, Esq. 

. Th. Bredichin. 
. W. Brushfield, Esq. 
^. E. Burton, Esq. 
TProf. A. Cayley. 
T. Croft, Esq. 
S. M. Drach, Esq. 
J. Dreyer, Esq. 
■J. Ennis, Esq. 
E. L. de Forest, Esq 
P. Gray, Esq. 
Mrs. Griesbach. 
Mods. A. Guillemin. 
J. Herapath, Esq. 
Lady Herschel. 
Prof: E. S. Holden. 
Rev. F. Hewlett, 
Mons. L. Hugo. 
Dr. Krueger. 
S. P. Langley, Esq. 
Lord Lindsay. 
Sig. G. Luvini. 



Mons. E. Mailly. 
S. H. Miller, Esq. 
Dr. C. G. Moesta. 
Mons. J. A. Normand. 
Prof. J. E. Nourse. 
A. V. Nursinga Row. 
Dr. Nyr6n. 
Dr. Oudemans. 
Rev. S. J. Perry. 
Dr. C. A. F. Peters. 
Mons. E. Plantamour. 
A. C. Ranyard, Esq. 
Padre Secchi. 
Mrs. W. Selwyn. 
Rev. T. Sheepshanks. 
Prof. P. Tacchini. 
Sig. G. Terapel. 
C. Todd, Esq. 
F. W. C. Traflford, Esq. 
Mons. P. Tremaux. 
L. Trouvelot, Esq. 
Capt. G. L. Tupman. 
Mons. E. Vicaire. 
Dr. H. C. Vogel. 
Dr. A. Wagner. 
C. V. Walker, Esq. 
T. Warner, Esq 
Rev. T. W. Webb. 
Major- Gen. Worster, 
Dr. R. Wolf. 
Prof. C. A. Young. 
Prof. K. W. Zenger. 



2 26 lAst of PubUc Insiituiimis Sf'c. - xxki 

Observatory, Cincinnati. 
' Observatorj, Coimbra. 
Observatory, Collegio Bomano. 
Observatory, Ley den. 
Observatory, Madrid. 
Observatory, Melbourne. 
Observatory, Milan. 
Observatory, Moncalieri. 
Observatory, Munich. 
Observatory, Prague. 
Observatory, Strasburg. 
Observatory, Sydney. 

United States Naval Observatory, Washington. 
Imperial Academy of Sciences, Berlin. 
Imperial Academy of Sciences, St. Petersburg. 
Imperial Academy of Sciences, Vienna. 
Royal Academy of Sciences, Brussels. 
Academy of Sciences, Paris. 
Academy of Sciences, Amsterdam. 
Academy of Sciences, Bologua. 
Academy of Sciences, Buda-Pesth. 
Academy of Sciences, Copenhagen. 
Academy of Sciences, Gottingen. 
Academy of Sciences, Montpellier. 
Academy of Sciences, Munich. 
Academy of Sciences, Stockholm. 
Academy of Sciences, Turin, 
Italian Society of Sciences, Rome. 
Pontifical Academy de Lincei. 
Society of Sciences, Batavia. 
Society of Sciences, Bordeaux. 
Society of Sciences, Cherbourg. 
Society of Sciences, Helsingfors. 
Society of Sciences, Leipsig. 
Society of Sciences, Zurich. 
Mathematical Society of France. 
Museo Fisico, Florence. 
Musee Teyler, Leyden. 
Bureau des Longitudes. 
Depot General de la Marine. 
Imperial University of Kasan. 
Italian Spectroscopic Society. 
Astronomische Gesellschaft, Leipsig. 
Berlin Physical Society. 

International Committee of Weights and Measures. 
Smithsonian Institution, Washington. 
American Academy of Sciences. 
American Philosophical Society. 
American Bureau of Navigation. 
Franklin Institute, Philadelphia. 



Feb. 1877. 229 



ADDENDUM. 

Hie Suspected IntrorMercurial Planet, 

The Astronomer Bojal has requested me to append to the 
Aimaal Report of the Council the following letter recently 
received from M. Le Verrier, relating to the approaching pos- 
sible conjunction of the supposed intra-Mercurial planet with 
the Sun on March 21, 22, and 23 next. It is of extreme im- 
portance that a continuovs scrutiny of the solar disk should be 
kept up, both in the northern and southern hemispheres, during 
these three days, as after 1877 no other opportuniiy will bd 
afforded for many years of observing a possible transit of the 
planet. The Sun's disk should therefore be watched for a small 
planet at every two hours or more on the three days mentioned 
above. Photographs should be obtained when practicable, as they 
are iBx preferable to eye- views. £. Dunkin. 

Fabxs: 15 Fhrier 1877, 

" MoNSiBUB BT Honors CollIigue, 

'' Yous n'aurez pas oubli6 qu*au commencement de Tautomne 
dernier une discussion s*61eva des observations faites k diverses 
^poques et attributes aux passages d'une on de plusieurs planetes 
BUT le disque du Soleil. 

" Apres une Elimination attentive des observations inconcili- 
ables, il fat reconnu que cinq observations pouvaient effective- 
ment appartenir aux passages d'une planete sur le disquo du 
Soleil, savoir : — 

Fritach 1802 Octx)bre 10 

Decuppis 1839 Octobre 2 

Sidebotham 1849 Mars 12 

Lescarbault 1859 Mars 26 

Luminis 1862 Mars 20. 

(Comptea Rendus de VAcacUmie, 
2 Octobre 1876, p. 649.) 

" n parut des lors difficile d'admettre que des observateurs qui 
n*avaient eu aucune relation entre eux, ni aucune conDaissance 
^ea periodes en discussion, fussent ainsi tombes par hasard sur 
cinq epoques precises d'un phenomene explicable par Je mouve- 
ment d'une meme planete. 

" Le savant directeur du Nautical Almanac, M. Hind, ajouta 
l^ucoup a Tautorite de ces conclusions, en montrant qu'une 
fiixieme observation (Stark, 181 9, Octobre 9) etait egalement 
i^presentee par la meme orbite. (Comjpies Eendtis, 30 Octobre 
1876, p. 809.) 

s 



230 The Suspected Intra^Mercurial Planet. xxxm. 1877 

" Les passages de la planete offrent des periodes comme tons 
les ph^nomenes du m^me genre. 

'* II a 6t6 etabli qu'elle sera en conjonction avec le Soleil le 

22 Mars prochain. Malheareusement les incertitudes qni regnent 
sar la position du noeud et la valeur de Tinclinaison ne permet- 
tent pas de decider si la planete passera pr^cisement sur le disqae 
du Soleil ; et Ton pent meme aMrmer qu*apres 1877 il s'6coulera 
plusieurs annees avant qu'un passage soit possible. Dans cette 
situation, les astronomes estimeront, sans doute, qu*il importe 
d'observer tres attentivement le Soleil les 21, 22 surtont, et 

23 Mars procbain. 

*' Yemllez agr6er, Monsieur et bonor^ coUegue, rassurance 
de mes sentiments d^voues. 

" Lb Vbbrieb." 

It may be remarked tbat telegrams on tbis subject bave been 
forwarded bytbe Astronomer Royal to Dr. Hector, at Wellington, 
and to Dr. Haast, at Canterbury, New Zealand ; to Mr. EUerj, 
at Melbourne; to Mr. Russell, at Sydney; to Mr. Todd, at 
Adelaide ; and to Mr. Pogson, at Madras. E. d. 



MONTHLY NOTICES 

OF THE 

KOYAL ASTRONOMICAL SOCIETY. 

Vol. XXXVIL Maech 9, 1877. No. 5. 

^BOFBSSOR A. CayTiBY, P.R.S., Vice-President, in the Chair. 

John Band Capron, Esq., Gnildown, Guildford, Surrey ; 
^- William Evans, Llanerchymedd, Anglesey ; 
. ^H,nk McClean, Esq., M.A., 23 Great George Street, West- 
°^ter ; and 

*- Meldola, Esq., F.C.S., 23 John Street, Bedford Row; 

^^^^ Piloted for and duly elected Fellows of the Society. 



The Nebula in Orion — Request to Astronomers. 
(Communicated by E. B, Knobel, Esq.) 

\ i,^^ engaged in observations of the central portions of the 
'^ ®7^1a of Orion f and desire to compare all former drawings, both 

^?^^^ and modem. I have in my possession the following 

^*^^^hed drawings of it :— 

^^56, Huyghens ; 1673, Picard ; 1731, Mairan ; 1742, Long ; 

T^5o, Le Gentil (2) ; 1771, Messier; 1774, W. Herschel ; 1779, 
tebvre; 1794, Schroeter; 1797-8, Schroeter (4); 1824, J. 

^J^chel; 1837, J. Herschel; 1837, Lament; 1839, De Vico; 

^^. Rondoni (2) ; 1847, Lassell ; 1848, W. C. Bond (2) ; 1854, 

j^ell; 1862, Liaponoff and Struve ; 1862, Secchi; 1862, 

,|^pel; 1865, G. P. Bond; 1867, Lord Rosse; 1868, Secchi; 

^^^, D' Arrest; 1874, Winlock and Trouvelot ; 1875, Holden 

^ Trouvelot. 
f Through the courtesy of the various authors, I have original 
republished) sketches, or elaborate drawings, made by 
^per(?); Schmidt, 1861 (2); Lassell, 1862; and Trouvelot, 



232 Mr, Stone y On Aj)parent Brightness xxxvn. 5, 

I shall be most grateful for notice of any drawing not men- 
tioned in the above list, whether published or unpublished, or for 
a reference to unpublished observations of this object, particu- 
larly of the central nebulous portions. 

Edwabd S. Holden. 

United States Naval Observatori/, Washington, 
1877, January 31. 



27^6 Approaching Opposition of Mars — Beqtiest to Astronomers. 

M. F. Terby, Doctor of Science, Louvain, Belgium, inyite^^j 
observers, particularly those in the equatoreal and soathenc: 
regions, to make a large number of drawings of the planet Mairs 
during the remarkable opposition of the present year, 1877. ^® 
recalls to them that he has published a Memoir, entitled ** Ar6o- 
graphic, on 6tude comparative des Observations faites snr 
Taspect de la planete Mars depnis Fontana (1636) jnsqu'li nos 
jours," t. xzxix. Mem. Caur. (4°) de TAcad. R. de Belgiqne. 
This Memoir contains a largo number of questions, which might 
be answered by the observers in the opposition of 1877 ; these 
refer to the principal doubtful points in Mr. Proctor's Chart 
M. Terby begs the astronomers who have hitherto kindly com- 
municated to him their observations to send him also their draw- 
ings of 1877 ; he hopes thus to perfect Mr. Proctor's already so 
excellent chart- 



The Dimccht Observatory Puhlications. 

Mr. Ralph Copeland writes to correct an error occurring in 
Monthly Noticeitf p. 1 99, where it is stated that the arrangement 
and reduction of vol. i. of the Diinecht Observatory Publica- 
tions were i)erfornicd by liim. Although he is responsible for the 
genei'al ari*angeraent of tlio work, yet the wliole of the computa- 
tions were performed by Mr. Robert Copeland, of Manchester. 



On Apparent Bnghtness as an Indication of Distance in Stellar 
Masses. By E. J. Stone, M.A., F.R.S., Her Majesty's 
Astronomer, Cape of Good Hope. 

In the important investigations of the motion of tbo solar 
system in space by O. Struve and Airy, the distribution of the 
stellar distances has been made in accordance with the views of* 
W. Struve. The correctness of these views has, from time to 
time,* been questioTiod. Tt may have been shown that some 



If arch 1877. as an IncUcaiion o/Distaiice etc. 333 

astronoiiifira have attacbed nndae importanoe to the nnmerical 
aocnracj of the resnlts obtained bj W. Strave; bat I cannot con- 
nder ihaJt the average distribation of the di&tances of stars 
fMXWidiDg to apparent brightness has been, or indeed ever will 
be, disproyed. I do not know that there is much novelty 
in mj views, but the subject presents itself to my mind in the 
following way. It is certain that the apparent brightness of a 
etBT will, ccRteris paribus^ vary inversely as the square of its dis- 
tance from us ; and an inspection of any table of annual parallaxes 
wiU prove that we have around us ample space for very consider- 
able variations in the magnitudes of stars from the sole effects of 
distance. 

The following table, extracted from Herschel's OuUiiies of 
Mrmmyf will be sufficient for my present purpose : — 



star's luune. 


Annual parallax. 


a CentEnri 


0-976 


61 Cjgni 


0348 


a Lyre 


0155 


SirinB 


0-150 


1830 Gruombridge 


(0-71) doubtful 


i Unne Mnjoris 


o>33 


Arctnnis 


0-127 


Polaris 


0067 


Capella 


0-046 



*^ithoQt attaching undue importance to the numerical accuracy 
of the smaller values, we have here a proved range of stellar dis- 
^Qcesinat least the proportion of i to 10. It is certain, there- 
fore, that our brightest stars might be changed to stars of about 
the tenth magnitude by a mere shift of our relative position in 
*P*ce. But there are not the slightest grounds for our supposing 
^t the relative distance of the stars from us is restricted to 
^7 8uch proportions as i to 10. Such a proportion merely 
^"^h the limit beyond which we cannot discriminate with much 
certainty between the distances of the stars. Annual parallaxes 
of leas than a tenth of a second of arc are sensibly equal, 
oocanse the limit of our present power of accurate measurement 
^heen nearly reached. If we assume, therefore, that the mag- 
Mtttdes of the stars depend chiefly upon their distances from us, 
our assQmption rests upon a vera causa, and we have independent 
P'oof of the sufficiency of the assumed cause to produce the 
observed differences in stellar magnitudes. 

Bat I think it may be shown that such an assumption is not 
* Dtere barren hypothesis. I know of no more striking fact in 
-^tronomy than the rapid increase in the number of the stars as 
^® proceed down the scale of magnitudes. Every increase of 

T 2 



234 -^^^ Stone, On Apparent Brighiness xxxni. 5, 

optical power appears only to bring this &ct into greater pro- 
minence. 

K we accept distance as the principal factor in determining 
stellar magnitudes, the rapid increase in the number of the 
fainter stars not only becomes intelligible, bat is a neoessary oaop 
sequence of onr assumption on the most general distribution of 
stellar masses which we can conceive. 

Suppose that there are n different degrees of intrinsic bright- 
ness in the stars around ns. Suppose, for the purposes of numerical 
illustration, that we have over any surface these classes of stars 
distributed in any definite proportions. Since the brightness of 
a star is classed under discontinuous magnitudes, we can logically 
suppose, for our present purpose, that the stellar distribution is 
discontinuous also over the surfaces of small portions of spheres 
whose radii are such that a star shifted from one sur&ce to the 
next would be changed one magnitude. With such a distriba- 
tion of stars, without any assumptions of uniform distribution in 
all directions or at all distances, and \rith any proportions 
amongst the stars of different intrinsic brightness which could be 
admitted as probable, the large increase in the number of the 
fainter stars becomes a necessary consequence of the supposed 
distribution. I shall, however, for simplicity, introduce the con- 
ditions that the stars of different intrinsic brightness are to be 
supposed equally distributed, and their number in any given 
direction proportional to tlie area over which they are distributed. 
Such conditions are certainly not strictly true, and so far as they 
are untrue their tendency will he to make the results of the com- 
putAtions based upon them differ from the results of observation ; 
but on the large average these conditions are probably close 
appi*oxi mat ions to the truth. Through our position conceive a 
cone of small solid angle to be drawn in any direction. Let 
a?! , ^2 • • • '^fi ^ the radii of the spheres which cut the cone at 
distances such that a star would be changed one magnitude by 
being shifted from one of the surfaces to the consecutive sur- 
faces ; ^1 being such a distance that the stars of the first degpree 4 
of intrinsic brightness will at that distance appear stars of the < 
first magnitude. Then, \^ dsi, ds^, . . . ds^ are the portions of the^ 
spheres intercepted by the cone, the number of the stars oft% 
tne different magnitudes in the direction under consideration^^ 
will be — 

1st magnitude number = C (some cons^taut). 

N ds^ (18^ dft^ ff«x/ 



nth 



C^bTch 1877. 08 an Indicaiiati of Distance etc, 235 



stars of the first degree of intrinsio brightness only ap« 
' of the first magnitude when found on dsy ; of the second 
tftACniitude on ds^ ; and of the nth on ds^. 

Stars of the second degree of intrinsic brightness appear of the 

second magnitude on cZ^i ; of the third on ds^ ; and of the (n+ i)th 

on ds^. Stars of the third degree of intrinsio brightness appear 

of the third magnitude on d$i ; of the fourth magnitude on ds^^ &c. 

Consequently, therefore, since a similar result holds in all 

directions, we have generally the number of nth magnitude stars 



. / d$. ds^ dsn\ 

\ asi ddx a«|/ 










It remains to determine the numerical values of the ratios in- 
▼dved. 

b Sir J. Herschel's volume of Gape Observations will be 
foond some experiments showing that, if the double star a 
Oentdurt be taken as the standard, the brightness of stars of the 
fint lonr magnitudes of the ordonary s^e are very approxi- 
maielj 

for I8t magnitude Bt&rs. 



(I-4I4)« 



(?ii4? ^"^ ^°^ " 



{ZAHf 



for 3rd 



(7iii7f-4th 



»> tl 



»» l» 



Such a scale will not, however, be true for the fainter stars. 

In the introduction to Carrington's Bedldll Catalog^ie of 
oian^ there are some results of experiments with varying aper- 
^^^^ showing that from the fifth to the ninth magnitude of the 
^^^^^^ scale the brightness of each magnitude is fairly repre- 
wnW by the relation 

Brightness of nth magnitude = 275 x that of (» + i]th. 

^ shall exhibit the proportional number of the stars of 
flilierent magnitudes when the ratios of — are determined with 

^ these light ratios. We must expect, if the supposed distri- 
*^tion is any close approximation to the truth, to find that the 
Jf^puted numbers will agree with the observed numbers, for 
pe first four magnitudes better with Herschers scale, and for the 
"^five magnitudes better with Carrington's scale, 



336 Mr, Stone^ On Apparent Brightness etc, . joxm. 5, 

Wiih Herechers scale 



5 



, I Vr4i4/ ' 



And the number of r^th magnitude stars 

CA 

'» " (7^4? ^^^'^^^^^ * (2-414)' <^ • • • • + »-4i4)'}; 

— - + 0-914 »2 + 0752 }{ !• . 

Next, assuming Carrington's light ratio, we have 

«, = C {I + 275 + (275)« + . . . . + (275)"-»} ; 
(275)»-i 



«« = C 



175 — 



The following Table exhibits certain numbers attributed ^ 
Argelander and the results of the two formulae. The number oi 
first magnitude stars is made equal for the purposes of 000^' 
parison : — 



[ag. 


Argelauder'g 
numbers. 


Computed numbers 
Herschers ficale. 


Computed numbers 
Carrington's scale. 


MeuoT 
Compd. 


I 


20 


20 


20 


20 


2 


65 


78 


75 


76 


3 


190 


195 


226 


210 


4 


425 


390 


642 


516 


5 


1,100 


683 


1.786 


1.234 


6 


3,200 


1,094 


4,931 


3.012 


7 


13,000 


• ■ • 


13.581 


• • • 


8 


40,000 


« t ■ 


37,360 


• •• 


9 


142,000 


• • • 


102,780 


• • • 



It will be seen that the numbers based on Hcrschers scale d 
agree best for the first four magnitudes, and those based on Gai 
rington's scale best for the fainter magnitudes ; whilst a mea 
between the two agrees best with the observed numbers for tl 
end of Herschers and the commencement of Carrington's seal 
This is what might have been expected. The computed numb 
of stars of the ninth magnitude falls short of the observed numb 
by forty thousand ; but when it is considered that this diser 
pancy is not greater than would arise from an uncertainty * 
estimation of about a tenth of a magnitude at the end of tl 
scale, the agreement between the computed and obsenri 
numbers will, I think, be considered sufficiently close to pro* 
that the supposed distribation of the stars must be a somewh 
close approximation to the truth. 

If the distribution which I have supposed be any do 



^^artsh 1877. -P*^/ Neweomb, On Obseriationa etc, 237 

^prozimation to tbe tmth, the average distances of the ftdnter 
^*^tiB must be greater than those of the brighter stars ; but it by 
^^ ^eaQB follows that any one £unt star is farther from us than 
^r^ one mncb briehter star. In fact, the supposition made has 
^^^^ that stars of all magnitudes may exist at all stellar dis- 

Observations of Contacts of the Limb of VetiuSy or Mercury, vnth 
thai of the Stm, "By Prof. Simon New comb. 

^<^ Daring the past four years, I have had occasion to give some 
V^'^ntion to the problem of obtaining accurate observations of the 
^^>ioa8 phases 01 contact between tne limb of an interior planet 
fV^^ that of the Sun. My views, as now presented, have been 
^. ^lived from the study of an artificial representation of a transit 
^ ^"^ VetiuSy aided by general considerations on the subject, and by 
^e opinions and investigations of others. I am induced to pre- 
^^nt them at the present time by the researches of M. Andr6, 
^^d the papers of Mr. Stone and Father Perry in the Monthly 
'^fottces for December last. 

(i) If I might be allowed to criticise certain of the views of 
^i^thers in a general way, I should say that one defect of much of 
^^ihe reasoning on this subject is this : it has too generally been 
^^ssumed that the geometric outlines of Veiiiis and the Sun, 
cx>iisidered as mathematical lines, can be noted in observation 
^^vitb the same sort of definiteness and precision as that with which 
^he mind conceives them ; and sufficient attention has not been 
-paid to the practical difficulties which the eye meets with in 
Tepresenting this geometric conception. I conceive that the 
question whether a certain phase can or cannot be definitely dis- 
tinguished and observed by the eye is to be settled by actual 
trial, and by a consideration of the imperfections of vision, 
rather than by a consideration of its purely geometric definite. 
ness of form. 

(2) One result of the trials with the artificial transit is, that 
there is a certain phase near that of external contact which can 
be observed with the same order of precision as the internal con- 
tact, provided that the proper conditions are fulfilled. Among 
these conditions are, that the observer shall previously have 
practised on the artificial transit ; that he shall know at exactly 
what point of the Sun's limb to look for the first contact ; that 
he shall know when to look for the contact with an uncertainty 
of not much less than half a minute, nor much more than a 
minute ; and that he shall have a telescope of fixed size and 
power. Of course the phase thus observed will not be geometric 
contact, but that occurring at the time when the notch in the 
Sun's limb first becomes visible. This phase varies much less 
with variations in the atmospheric condition and in the size and 
power of the telescopes than might have been supposed. 



238 Trof. Newcomh, On Observations of XXXTIL 5, 

(3) The pliase of external contact at egress is more ^noe^ 
tain than at ingress, owing to the doubt of the observer as to 
whether the notch has or has not disappeared from his viewv 
that doubt extending over a longer period than the doubt as to 
when he first sees the notch at ingress. 

(4) Referring now to the spectroscopic observation of the 
external contact, and to Father Perry's suggestion for rendering 
the projection of the planet on the chromosphere visible In 
means of a coloured glass in order to observe this contact, wkidi 
two methods arc the same with respect to the optic phenomeOi 
designed to be produced, I do not think it possible to obtain 1 
precise observation in either of these ways. The phenomenon ic 
be observed would then be the cont6x;t of a dark limb (that oi 
the planet) with an adjacent bright limb (that of the Sun), on i 
background intermediate in tint (that of the chromosphere). Th< 
result must then depend very largely on the amount of irradiatiiNi 
and on the observer's acuteness of vision in seeing the slowl] 
diminishing line of chromosphere between the planet and the Son 
The planet will, in reality, be invisible : all the observer can sei 
will be the outline of the chromosphere, as cut out by the planet 
and when the latter gets so near the limb of tne Sun thttl 
the chromosphere itself is invisible — owing to the overpower- 
ing brightness of the Sun's limb — the outline of the planel 
can no longer be traced, and will not reappear until it 11 
seen projected on the background of the Sun itself. I conorivc 
therefore, that any attempt to make different observers certain} 
note the same phase of such a phenomenon will result in failnit 
It would, however, be of interest to try the method artificially. 

(5) In describing the phenomena near the time of intenu 
contact, I shall consider the planet to be approaching egrea 
For reasons which I shall soon mention, the artificial transit "wi 
placed at a distance of about eleven hundred yards from the plai 
of observation, so that a greater or less amount of atmospher 
undulation was always present. Supposing, then, that the plan* 
was approaching the Sun's limb, and the thread of light growii 
thin, owing to the approach of contact, the first thing which f 
observer would remark was that, in consequence of the constai 
changes of outline caused by atmospheric disturbance of tl 
images, no set of phenomena could be described as invariabl 
It would be necessary to combine judgment with sight, I 
considering what might be called a mean phenomenon. Differei 
observers might form different judgments as to what this met 
phenomenon was. It would, however, always be seen that as tl 
thread of light became quite thin, it looked darker than the re 
of the Sun ; and unless the atmosphere was more steady than 
usual in the day-time, the line of light would occasionaUy 1 
broken up into two or more very irregular threads or twists of Ugh 
which would gradually grow fainter until they would occasional! 
almost disappear from view. Repeated trials showed that tl 
time of true internal contact was marked by the moment i 
which light entirely ceased to glimmer across the dark spac 



kieh 1877. CoHtacts of Venus or Mercury etc. 239 

nned by the approach of the limb of the planet to that of the 
in. 

(6) Every attempt to estimate an apparent contact, or 
oxneat at which the limbe of Venous and the San were tangent 
» each other, without reference to the appearance of the thread 
r light, was a total failure. It was, in fact, impossible to make 
ny sach estimate without an uncertainty of half a minute or 
nore. This will not appear surprising if we reflect that the out- 
ines of Venus and the Sun cannot present themselves to the 
?inon as geometric lines, but only as more or less indefinite edges 
of a visible surfiEM^e of sunlight ; which visible surface disappears 
niofii gradually near the region of contact, and, in fact, at the 
Doment of idettl " apparent contact '* cannot be seen at all at the 
point of contact. Anyone who wishes to satisfy himself on this 
point has only to examine a series of figures in which the black 
drop is represented, and try to decide which of them represents 
Apparent contact. If he wishes to come as near nature as pos- 
sible, he must shade off the outlines both of Venus and the Sun, 
80 tibat they shall terminate in a soft border, and view the 
pictue through a rising current of hot air. 

(7) Any artificial representation of these phenomena, in which 
the Wght surface of the Sun is surrounded by a dark back- 
groond, must fail to be correct in a very important particular. 
As a matter of fact, we know that the atmosphere immediately 
Aionnd the Sun's limb is of dazzling brilliancy. In meridian ob- 
wmtions of the Sun, when the light is so cut down by a dark 
glttB as no longer to dazzle the eye, the five spider-lines are 
yuiUe on the Iwu^gpround of the atmosphere ; else it would bo 
^'^Wfiible to observe the transit of the Snn's first limb. This 
Mliancy of the atmosphere must greatly diminish irradiation ; and 
u the San is observed through haze (as must often be the case in 
o|*W7ations of contact when the San is near the liorizon), irra- 
^i*^n may be entirely destroyed. It will therefore be ira- 
pottible to observe an actual internal contact of Vanus or 
^frcury with a precision corresponding to that of an artificial 
<^tact on a black backcround. 

(o) The atmosphere affects the phenomena of contact in* 
three w^b : — 

fl- By illuminating the background as just described. 
fi» By producing undulations in the outlines of the images, 
thereby preventing the phenomena from being invariable, 
y. By softening the outlines of the Sun's limb, and thus 

rendering it more or less indefinite. 
The artificial transit to which I have alluded was placed at a 
T^tance, in order that all these effects might be produced and 
*tiiaied; otherwise, the optic phenomena of contact may bo 
entirelj different. For instance, because the black drop is 
Hharplj seen in the artificial transit when the background is 

joite black, it does not follow that it will be noticed in the actual 

transit. 

(9) A good idea of many of the causes of uncertainty to 



240 Frof. Newcomby On Observations etc. XXXTIL 5, 

which I have allnded may be formed by examining a series of 
photographs of internal contact taken by the Janssen procesB. 
One will immediately appreciate the distinction on which I h^Ye 
insisted, between geometric lines on the one hand and the out- 
lines of Vefius and the Sun on the other. 

(10) I have said little of the black drop ; partly because I do 
not think there can be mnch room for a real difference of opinion 
respecting its nature and causes, and partly because the question 
whether it is seen is of entirely secondary importance, except as 
affording some indication of the sharpness of definition. In 
looking at the artificial transit, it was very easy, about the 
moment of internal contact, by taking a general mean outline of 
the undulating image of the planet, and imagining that outline 
continued across the undulating line of light and darkness mixed, 
into which the ideal thread was reduced by the imperfections of 
vision, to see something like a black drop. On the other hand, 
another observer, with his attention fixed solely on the thread of 
light, would see nothing of the sort. The final disappearance of 
the thread of sunlight being the only phase which can be actually 
observed, an observer fixing his attention exclusively on this 
would not see any black drop at all, unless the amount of irradia- 
tion was exceptionally great. 

(11) I see little or nothing in Mr. Stone's views radically 
inconsistent with those which I have here set forth. His remark 
on his observation of the egress of Veuus in 1874, " the apparent 
contact was rendered more difficult than would otherwise have 
been the case by the appearance of this ligament, or, in other 
words, by the disappearance of a sensible portion of the Sun's 
limb near the point of contact," is in entire accord with the 
views I have expressed in paragraph 6. 

(12) The general conclusion to which I am led is that theVe 
is but one phase of each contact which can be observed with any 
approach to accuracy, namely : — 

a. The time when the notch made by Venus advancing on 

the Sun becomes visible. 
/3. The time at which tme sunlight is first seen all the way 

around the following limb of the planet, 
y. The planet approaching egress, the time when it first 
completely cuts off the true limb of the Sun, and the space 
connecting the limb of the planet with the sky becomes 
as dark as the planet itself. 
^. The time when the last limb of the planet, leaving the 

limb of the Sun, disappears from view. 
If an observer, at the time of internal contact, does not note, 
or try to note, the phases /3 and y, there is no definite phase to 
which his observation can be referred. The old notion that at 
second internal contact there is a sudden formation of the black 
drop, which marks the moment of true contact, has been so com- 
pletely exploded that it needs no further refutation. The more 
clear and dark the atmosphere aix)und the Sun, the more rapidly 



Maieh 1877. Mr, Marth^ Ephemeris etc. 241 

will contact appear to form, whether a black drop is seen or not ; 
bat under no oircumstances nnder which an actual transit is likely 
to be observed for parallax will it be really sadden. When it 
appears so it ia only because the observer failed to notice the 
gradaal darkening and breaking np of the thread of light. From 
the oommenoement of this darkening and di£fasion, until the 
** apparent contact/* which comes last of all, there are a series of 
pTOgrefisiye changes, which may extend over a period ranging 
anywhere from twenty or thirty to ninety seconds, at any point 
of which a random obeenration of internal contact may fall. The 
wone the definition, and the lower the planet, the greater the 
nu^; but the time of true contact is always near the mean of 
theperiod. 

Watkmfftam, 
1877, February 22. 



Ephemerisfor Physical Observations of Jiqnter 1877. 

By Mr. A. Marth. 



Xon. 


AiuciD wa 

poiitkmaf 


MeiidiMi directed 


Latitude of 


Annual 


Eqnatoreal 


X877. 


ITiAzis. 


totlieBarth. 


Eitrth 


1 Sun 


Parallaa 


u 


Diameter. 








difL. 


aboye %'. 


9 Equator. 


































M«.3i 


35772 


104-8 




-2-31 


-2-45 


- IO'8l 




3871 


A». 




4353*1 






+ 


*I4 




Apr. 5 


35759 


137*9 


3*2 


231 


243 


1067 


-21 


3933 


10 


357*51 


171-1 


3*3 


230 


242 


10-46 


•29 


3996 


«5 


35746 


2044 


3*3 


230 


2*41 


1017 


•37 


4059 


ao 


357-44 


237*7 


3*4 


229 


2-39 


980 


•45 


41*22 


25 


35746 


271-1 


35 


2-29 


238 


935 


•53 


4185 


30 


35752 


304-6 




229 


237 


882 




4246 


3Uy 5 


35761 


3381 


35 
3*6 


-228 


-2-35 


-8-21 


•61 
•67 


4304 


10 


35774 


117 


3*6 


228 


2*34 


754 


•75 


4360 


^5 


357*90 


45*3 


3-6 


2-28 


2-32 


679 


•82 


4413 


30 

1* 


35809 


789 


37 


228 


2-31 


5*97 


•87 


4460 


25 


358-31 


1 12-6 


3*7 


228 


230 


510 


•93 


4503 


30 


35855 


146*3 




228 


228 


417 




45-40 


June 4 


358-82 


1800 


3*7 
3*7 


-2-28 


-227 


-3-20 


•97 
roi 


4569 


9 


359* 10 


2137 


37 


228 


2-25 


2*19 


103 


45-92 



242 



Mr. Marihj Ephemeris etc. 



XXITU. 5, 



Greenwich 


Angle of 


Longitude of X'b 


T^iAtv'*^ mf 








Noon. 


position of 


Heridian directed 


iifhlH 


•«aH> yr^ 


Annua] 


L ■ ] 


Bqnaloni 


1877. 


U'B AziA. 


totbeEsrih. 


Earth 


1 Son 


Buallaz. 


^anileK 


w W 




diff. 


aboye X*i 


s Equator. 































June 14 


359*39 


247*4 

3*7 


2-28 


2*24 


i-l6 


1*04 


4607 


19 


359-68 


28ri 

3-6 


2-28 


2-22 


— 0*I2 


i-os 


46-14 


24 


35998 


3147 
3-^ 


2-28 


2*21 


+0-93 


1-04 


4613 


29 


0-28 


3483 

3'5 


227 


2-19 


1*97 


1*01 


46-os 


July 4 


0-56 


21-8 

35 


-2-27 


-2-i8 


+ 2-98 


•99 


45« 


9 


083 


55*3 

3*4 


2*26 


2-i6 


3*97 


•95 


45-64 


14 


108 


887 

3*3 


2-26 


2*15 


4*92 


•89 


4S-33 


19 


1-31 


I22'0 

3*2 


2*25 


2-13 


S-8i 


•84 


44*95 


24 


1-51 


155*2 

3*1 


2*24 


2*12 


6-65 


77 


4452 


29 


r68 


1883 

3*1 


223 


2-10 


742 


71 


44-04 


Aug. 3 


182 


221*4 

2*9 


-2-22 


-208 


+ 8-13 


•64 


4353 


8 


1*93 


2543 

2-8 


2*21 


2-07 


8-77 


•56 


42-97 


13 


2*00 


2871 

2-8 


2'20 


2-05 


933 


•4» 


42-40 


18 


203 


319*9 

2*6 


2-19 


203 


9-81 


•40 


41-80 


23 


203 


352*5 

2*6 


2*18 


2'02 


10-21 


•33 


41*20 


28 


1-99 


251 

2*5 


2-17 


2X)0 


10-54 


•25 


40-59 


Sept. 2 


1*91 


57*6 

24 


-2-15 


-1-98 


+ 10*79 


•17 


3998 


7 


I 80 


900 

2*3 


214 


1-97 


10-96 


•10 


39-38- 


12 


1-66 


122*3 

2*2 


2-12 


1-95 


11-06 

4 


■ -03 


38-783 


17 


1-48 


154*5 

2-2 


211 


1*93 


11-09 


• -04 


38-2CE: 


22 


127 


1867 

21 


2-09 


1-92 


11-05 


•II 


37-6^ 


27 


103 


2188 

20 


2-07 


1-90 


1094 


•17 


37-i« 


Oct. 2 


076 


250-8 

20 


— 206 


-1-88 


+ 1077 


-22 


365^ 


7 


0*46 


2828 

1-9 


2-04 


1-86 


10-55 


•28 


36-0- 


12 


013 


314*7 

4351-9 


202 


1-85 


10-27 


- '34 


35-6^ 


17 


35978 


3466 


200 


-1-83 


9*93 




35L-^ 



Assumed daily rate of rotation 8 70° '60. The " annual par- 
allax " is the difference of the .lovicentric longitudes of the Sui» 
and EJarth, reckoned in the plane of Jupiter's equator. 



HaTch 1877. Mr. Hind^ On Two OccultaUons etc, 243 

The inclinaiiioiis y and the ascending nodes F of the orbits of 
the satellites in reference to the plane of Jupiter^ 8 equator are 
the following, the nodes being reckoned from the point of the 
'^mal eqninox of the planet : — 

^^. Sftt^L Satn, Sat. in. Sat.IY. 

7i r, 7, r^ 73 r, 7, r, 

'^» o 00 00 00 o 

^^- I 00098 40-9 0*4510 4952 01990 274-46 03298 330-54 

'^^'^•ao 98 39-5 -4518 47*51 '1981 273*91 '3290 33053 

^629 98 37-9 4525 45*49 -1972 273-35 '3281 33050 

^•28 98 362 4532 43*47 '1964 27280 3274 33045 

^^ 27 0*0098 34*5 0-4539 41*45 01956 27224 0-3267 33039 



J 



^» Two Ancient OccuUations of Planets by the Moon, observed by 

the Chinese. By J. R. Hind, F.R.S. 

In the Appendix to the Oaiinaissance des Temps for 18 10 will 

Z^ ^onnd a considerable nnmber of observations taken from the 

^bitiese astronomical records by the Jesuit missionary Gktubil, 

^^bofle manuscript relative to the Chinese observations of comets 

^'^s 80 much used by Pingr6 in the preparation of his Gotneto- 

^<zjjAi6. Amongst the numerous occultations comprised in this 

™^, there are two, and two only, in which the hour, or rather 

*Q^ particular two-hourly interval, at which the occultation 

^^^<>k place is distinctly stated, and it is to these occultations that 

^^^ present Note refers. 

I have calculated the circumstances of these phenomena with 

.™^ view to check a system of lunar motions previously applied 

J^ searching for the dates of several solar eclipses recorded on 

J^^ Nineveh tablets, to which my attention had been directed by 

^^^- J. W. Bosanquet, and which, as compared with several his- 

^^^**ical total eclipses, of which the dates are well known, appeared 

2% >^uire but small modification. I have employed Damoiseau's 

g^^1)le8 of 1824, adapting his main arguments to the results for 

J^^^^lar motions &c. obtained by the Astronomer Royal from the 

J ^^^cnssion of the Greenwich lanar observations from 1750 to 

30, retaining the last values given by Hansen for terms depend- 

^ on the square of centuries, which I had found to fit in best 

Sth the Greenwich motion proportional to time, at least as 

gards the secular acceleration. For the Sun and planets Le 

«rrier*s Tables were adopted. 

The earliest occultation recorded by Ganbil is one of the 

at Mars by the Moon, and is thus translated : — 

" Dynastie des Han occidentaux, la coar a Si-gau-fou da 

hen-sy. An 69 (B.c) = i" anneo Tutsiey i'* Lune, jour vou-mi, 

, 14 fevrier) ^ la 2' veille de 9 a 11 heures du soir, la Lune eclipsa 

-^(irsy eutro les constellations Kio ot Kang,*^ 




i 



244 



Mr. Hind^ Chi Tuh) Occtdtatians etc. xxx?lL 5, 



B.C. 69, February 14. 



Pans 
M.T. 
h 

2 


San*8 Tme 

Longitude. 
t It 

322 52 199 


Log. B. 
99979038 


h h m ■ 
Sideral time at 21 23 31 


6 


323 2 169 


99979208 


Equation of time i? '3 
(dabtnictive ttom Mean IMme] 


h 


MAn*HeUoc 

Longitnde. 
# // 


Han'HeUoo. 

Latitude. 
$ II 


Man' log. 
Bad.yeet. 


2 


166 58 505 


+ I 20 50*0 


0*2062127 


6 


167 2 444 


+ I 20 447 


0*2061696 


h 


Man* Apparent 
R.A. 

1 H 


Man* Appaxent 

DecL 
/ It 




2 

6 


196 49 44 

196 49 51 


-4 2044 
-4 20 38 


Log. distance 9'90774. 


h 


Moon*i ILA. 
t ti 


Moon's Decl. 

C 1 II 


/ // 


5 


196 49 27 


-3 46 31 


Hor. Parallax 60 8-5. 


6 


197 23 58 


-3 57 50 


Semi-diameter 16 23. 



I take the position of Si-gan-fou from M. Biot*8 Dtdior^ 
natre dee Nmns Anciens et Modemes des Villes et Arrondissemenr: 
de V Empire Ohinois — 

Long. io6<> 37' 45" E. of Paria; Lat. 34® 16' 45"; 

and from the above data find a visible occultation : — 

h m 
Immersion February 14 at 10 22 \ 

^ . I Apparent time at Si-gan-fou. 

Emersion „ ., 10 59) 

The immersion is therefore made to occur well within the 
two-honrly interval named in the Chinese annals, and the Moon 
was in Virgo, between the constellations Kio and Kang, 

The second occultation to which I have referred is one of the 
planet Vcnuii, thus given by Gaubil : — 

" Dynastie des Tsin orientaux, la cour i\ Nanking, appele alora 
Kien-Kang. An 361=5* annee, i*^ Lune, jour y-tcheou (20 
Mars) a I'heure irJmi (temps de 7 a 9 henres du matin), la Lane 
eclipsa Vcnn^t dans la constellation Goeijy 

Calculating in the same manner as before, I find the following 
figures : — 



Paris 
M.T. 

h 

12 

13 



Sun's True 
Tiougitudc. 

O I II 

359 47 396 
359 50 6-2 



A.D. 361, March 19. 

Log. R. 

h h m 8 

0*0018164 Sideral time at o 23 49 28 



00018113 



Equation of Time 7 49 

(^Siil'tmotivp from Mean Time). 



Ma«x5h 1877. Tkd Astronomer BoycU, On New Lunar Theory. 245 



13 



h 
12 

»3 



VeDtts* HeUoc. 
Loogitiide. 



tt 



»3 



239 o 56-6 
239 4 54'3 

Vemu^ jLppsrent 

bJL 
317 36 26 

317 39 14 
Koon*B ILjL. 

O t It 

317 4 23 
317 41 17 



Venae* Helloc. 
Latitadc. 

o / /' 

+ 09 55*5 
+ 9 41-0 



Venus* Log. 
Rad. Vect. 

9-8614762 

9-8614777 



Venus* Apparent 
DecL 

O f It 



-16 18 37 
-16 17 59 



I Log 



. distance 9*94883 



Moon's Decl. 
e # /# 

-15 45 55 
-15 38 21 



// 



Hor. Parallax 59 58 
Semi-diameter 16 20 



^ ^aJdng the posiidon of Nanking from the Oonnaissance dee 
•'^»»*p«j a visible oconltation again results :^ 



h m 
Immersion, March 19 at 19 34' 



(Apparent time at Nanking. 

^-^'i^aequentlj the phenomenon occurred within " Theure tchin,** 
^? ^"^eoorded by the Chinese, and the Moon was at the time in 
^^ ooDstellation named. 



-^^ote by the Asironomer Royal on the Numerical Lunar Theory. 

li the Monthly Notices of the Royal Astronomical Society for 
"* 4, January, vol. xxxiv., No. 3, T gave as the three equations 



^notion in the Lunar Theory the three following: (i) The 
.^l^^-ation of areas described by the radius vector parallel to the 
^^^^'tie of the ecliptic ; (2) The equation of vis viva parallel to the 
*^^^^ie of the ecliptic ; (3) The equation of motion perpendicular 
'^ plane of the ecliptic. 
It now appears preferable to substitute for (2) the equation 
^'^ ^ial forces parallel to the plane of the ecliptic, which may 
^ called (2*), and which is easily found to be the following: — 



I 

1 



-^J! fa! f* 






a'V ^+f^' a 






cos* 1 



2 1/ 



+ — • - • - • cos 1 , 
a a a 



246 



7^ Astronomer Boyal, Oral 



xxxra. 5, ^ 



and the right-hand side of equation (2*) appears to consiBt 
the following terms : — 



<'-my<iy-(i)'-&)' 



X • 



5 (sin « . cos* r . sin 1/ + cos • . sin 1'. cos Vy 
— 2 (sin u . cos' r . sin t/ + cos c0 . sin 1' . cos n sin « . sin tf 
—cos* I' 



f^.•(ly•©'•Sy43cosM^co.*^^Irh^^ 



^fL.izJ^.±.(A^\\(s:\\(rl\' 



I - 1 5 cobM' . COS* I t;-V I + ^ 008 r . cos I e;' - V I + 3 cos* V . coe fi^^V 



^A'« (€+m)' \A7 \K7 \aj V/ 



X I +^ cosM'.cos« It^Tv^-- ^ cosM'.cos' [iT^ --^ cos* l^coe* \7^-V] 

X |-is.co.s« k-V'l .sin |V'"^^| + 38in [V^K||; 

dv 
and there are no terms multiplied by -7-. 

at 

1877, 3f<:/rcA 5. 



The Astronomer Royal, in an oml address, adverted tcT 
M. Lc? Verrier's investigations on the possibility of discovery of 
an intra-mcTCurial planet, and to his issue of a circular i^. 
questing that observations of the Sun's disk for the passage ol 
such planet might be made on March 21, more paiticularly on 
March 22, and on March 23. He pointed out that for observa- 
tion of a transit whoso time could not be even approximately 
predicted, but which certainly would occupy only two or three 



248 Mr, Neisoitf On the Lunar Fertiirbationa etc. XIXYIL 5, 

On the Lunar Perturbations annngfrom the Planet Jupiter, 

By E*. Neison. 

Shortly after the appearance of Professor Newcomb's paper 
" On a hitherto unnoticed Inequality in the Longitude of the 
Moon" {Monthly Notices, Jane 1876, p. 358), my attention was 
directed to a new term in the lanar longitude arising from 
the perturbing action of J%ipitei\ and having the value 

— i"-0 8in {(2— 2OT, -<?) n^+/-2/, + A}. 

where (ti/-f/) is the Moon's mean longitude; (cn<+/— A) the 
Moon's mean anomaly; and (wiiw^-f/i) the mean longitude of 
Jupiter, This term agreed well in period with the inequality 
discovered by Professor Newcomb, and its coefficient was only 
a little smaller, but was stated to be merely approximate. 
Being at the time engaged in a similar branch of the Innar 
theory, I was led to examine this new term and to determine its 
value with some accuracy. 

This term arises from a portion of the disturbing function of 
the Moon due to the planets, which has not been examined by 
Laplace, Plana, or Pontecoulant, nor apparently by Hansen, 
namely, that portion depending on the difference in longitude of 
the Moon and planet. It is in form analogous to the evection^ and 
obtains its sensible value from the approach to equality between 
the periods of the revolution of the Moon's perigee and of the 
orbital revolution of the planet Jupiter, This fact at once 
directed my attention to the associated inequality of long 
period whose argument is — 

{(2-2W, -2(r) w^ — 2/, + 2A}, 

the value of which is still more dependent on the periods of the 
revolution of the Moon's perigee and the orbital revolution of 
the disturbing body. 

In the ordinary lunar perturbations arising from the disturb- 
ing action of the Sun, the value of the inequality of long 
period is less than one-twentieth of the associated inequality of 
short period, because the period of the revolution of the Moon's 
perigee is nine times as great as the period of the apparent 
motion of the Sun. In the perturbations due to the disturbing 
action of the planet Jupiter^ aa the period of the revolution of the 
Moon's perigee is nearly fonr-fifths of the period of the revolu- 
tion of the planet in its orbit, from the much closer approach 
to equality bistween the two periods, it is very probable that the 
inequality of long period would be almost as great as the 
associated inequality of short period. 

The determination of the accurate values of these two tdrms 
with algebraical coefficients was found to he a work of unex- 
pected difficulty and much labour. These and similar terms due 
to Jupiter rise by two orders on integration. As the ordinary 



187 7* Oapiain Tupman^ Oorrections etc. 249 

pertarbations only converge by. the same amount for each 

owcfT of the disturbing force of the Snn, it is necessary to take 

nto <5on8ideration the fourth power of the disturbing force of the 

Slim together with the first power of the disturbing force of 

Jw^ier. After satisfying myself that both inequalities possessed 

a Bensible Talue in comparison with the other inequalities 

uising from the action of the planets, the task of completely 

determining the Talue of these terms was postponed until the 

oonpletion of my new Tables of the general development of the 

liigher powers of the disturbing forces in the lunar theory. 

These Tables have been now finished sufficiently to enable 
tibeni being used to compute the value of these two inequalities, 
a work now of comparatively small trouble and difficulty ; and 
ibe algelvaical coefficients obtained, which are lengthy, have been 
rednoed to numbers. The results are — 

>r « - o'*493 «* {(2 — 2m,— c) » ^ + /- 2/, + A} 

+ 0^'-00I C08{(2 — 2»f| — 2C)*l^ — 2/, + 2A}. 

J»B -0^*990 Bin {(2- 2^1— e)n^ +/-2/, + A} 

+ i"'Si3 Bin {(2— 2W, — 2c)»^ — 2/, + 2A}. 

It is of course only in the longitude that these terms could 
become sensible. The labour in properly computing the value 
rf these terms is shown by the fact tliat it cannot properly be 
fene nnless over twenty similar terms have had their values 
prerionsly ascertained. 

These two new terms derive additional interest from the 
ict that they are the first terms derived from the second 
pwtion of the disturbing force of the planets which have been 
lound to possess sensible coefficients. They, moreover, have con- 
siderably larger values than any other inequalities due to Jupiter, 



^^edioru to the Nmitical Almanac Places of the Moon for 
^^Uude Ohservatiovs in connedimi with the Transit of Venus 
1874. By Captain G. L. Tupman. 

{Communicated by the Astronomer Royal.) 

, These corrections have been deduced entirely from obscrva- 
*wn8 at places which have been connected by galvanic sip^nals 
jnth the Royal Observatory, Greenwich, for longitude, and where 
both limbs of the Moon were equally observed, viz. : — 

I** of both elements at Greenwich, with the Transit-Circle and 
Altazirantb, between 1874, Sept, 15, and 1875, Feb. 23, 

2**of both elements at Paris, between 1874, Sept. 14, and 1875, 
^w. 22, including those made with the Gambey instruments, 
Published in Gomjites Bendus 1875, ^^^J 24. 

U 2 



250 Gapi, Tupman, Corrections to N,A, Places of xxmi. ; 

3° of Right Ascension at Konigsberg between 1874, Sept. ic 
and 1875, Feb. 26, pablished in the Astronomisclie NachricJUen^ Noi 
2020 and 2050. 

4° of Bight Ascension at Strasbnrg between 1874, Oct. 21 
and 1875, ^®^' 2S» Astronomische Nachrichten, No. 2050. 

5^ of North Polar Distance at the Radcliffe Obseryator} 
Oxford, between 1874, Sept. 18, and 1875, J*^* 2i/*t 

The published errors of the tabular B.A. at Konigsberg diffie 
considerably from the errors obtained at the other observatorief 
and the discordance appears to vary with the Moon's declioatiot 
as if the instrumental corrections were imperfect. As, howevei 
the observed E».A.s of the stars observed near the Moon are als 
given, new errors of the tabular R.A. were determined in tfa 
following manner :— 

The apparent R.A. of every star at transit over the Meridia 
of Konigsberg, founded on a mean R.A. derived from the Greei 
wich Catalogue for 1864, or, in defanlt, i860, was computed an 
compared with the observed R.A. A correction for the day we 
thus obtained from each star, and the mean from all the sta: 
was applied to the observed R.A. of the Moon's limb. 

The tabular R.A. of the limb was then interpolated wi" 
fourth differences from the section " Moon culminating Stara 
in the Nautical AhnanaCy adopting for the longitude of Konig 
berg Observatory i^ 21™ 59*32, which results from galvaiB 
signals, viz. :— 

Brussels east of Greenwich 17 28-90 {Roj/al Obs, M88.) 
Berlin east of Brussels 36 642 {Astr. Nach. XLV. 225). 

Konigsberg east of Berlin 28 24*00 (Astr. Nach. LVII. 350). 

Thediflference between the interpolated R.A. and the observed 
R.A. corrected as described above was taken as the error of the 
tables. 

A similar comparison of the observed and tabular R.A. 0I 
stars observed near the Moou at Strasburg showed no systematic 
discordances ; the published corrections were therefore adopted 
as were also the Pans corrections. 

The mean correction for each day, allowing half weight to thi 
Greenwich Altazimuth and the Konigsberg observations, wat 
then plotted off on charts of ruled squares, treating the R.A. anc 
N.P.D. separately, and a free curve drawn through all the points 
The adopted position of this curve among the points was sub 
mitted to several persons for criticism, and is believed to give th« 
corrections as accurately as the observations admit. 

Professor Newcomb's corrections were then plotted off on th< 
same charts, and as the " observation-curve " was weak at th< 
beginning and end of each lunation, it was made parallel t( 
Professor Newcomb's. 

The corrections taken from this modified portion of the curvi 
are denoted by an asterisk (*). 

t The Washington Obsenrations liad not been received at Greenwich v' 
the corrections were determined ; they would have been a valuable additf 



Uar'oli 1877. Moon in eonnecium with Tramii of 1874. 251 



P? + + + + + + + + + I I 



Is 
00 



VO M M 00 M O 

• ••••• 

ro ^ ^ fO fO W 

I I I I I I 



*l I *l '1 *l *l '1 '1 I I I I I I I I I I 






r 



+ + + + + + + +IIIIII 
* * * * 

*l *l '1 *l *l *l I *l "1 *l I I '1 *l 



I 




N 

09 







5S5 



V P5 



O 000 100 O »i^^r^O »^0 

• • m •,• • • • • • • • 

+ + + + + + + + + II 



I 



^ 4c 9^ 4* 

• ••••••••■••• 

I I I I I I I I I I I I I 



+ + + + + + + + + + + + + 






5 ^ ^ 






I I I I I I I I I I I I I 



t^ p v^ o r* p f^ 

b N fO in »n vb in 
+ + + + + + + 



p 

to 


• 




• 


to 

• 
^4 


• 




1 


I 


1 


1 


1 


lie 




a 


CO 


00 



:^ 5^ 



I I I 1 I I I 



I 



o ^ 00 «i^ 
to m m VO 



I I I I 



• «••••••••• 

II + + + + + + + + 



t>,00 Q N* N fOrfu^t^OvNvO 
'1 I I '1 *l *l *l '1 "1 '1 I '1 



^5 



OnO "^ N fOTfmvo t^OO 



ON O '-' <^ *^ ^ 
M W « w N c^ 



252 Capt, TupmaUy Corrections to N.A, Pltices of 






00 






VO ti^ ti^ 



f»* J B CO ro to 

Q* • • • 

III 



\ 



• 


to 

• 


P 


• 


• 


• 


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vr> 





• 


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1^' 


PO 


to 


N 


N 


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M 


• 


6 


6 





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1 


1 


1 


1 


1 


1 


1 


1 




+ 


+ 


-';i- 














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4> 


It 


* 


It 


• 


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N 


t^ 


CO 


t^ 


c« 





Pm 


00 


VO 


VO 


VO 


■ 


• 


• 


• 


• 


.-* 


:* 


to 

• 


to 

• 


• 


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• 


h r^ 


1 


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1 


1 


1 


1 


1 




1 


1 


1 


1 






00 



»^ M M P >0 

• • • •^ • 

>o »^ t^ t>» >o 

I I I I I 



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I i**^ t^ t^ O VO \r\ \r\ 

Irs* • • •• • • 

I I I I I I I 



i 



< C*« O O VO ro 00 

.4 < • • • • • 

.^ M o M M d ei 

i + fill 



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• ••••• 

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P « »^ op 
|5Z5 + + I 



CO ^ VO VO 

• • • * 

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I I I I 



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I I I I I I i 





00 

• 


• 

VO 


in 


• 


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p 

fO 




f 


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p 


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5 

a 



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> 

o 



p ►^ p op ir> p 
CO fO CO ^ C4 C4 

I I I I I I 



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»o to 



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VO 10 VO lo »r> w 

• • • • . • 

I I I i I I 



VO « ^ to CO O 

^ ;^ ^ ^ ;^ 5 
I I I I I I 



VO <o Ov to CI 00 
VO VO to VO VO 'T 

•••••• 

i I I I I I 





t>. 


vO 


0. 


f^ 


N 


vp 










N4 


6 





hi 


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VO 


CO 


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■ 


VO 

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to 




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W CO ^ to VO «*• CO 



^ai-eli 1877. 



bo 



S ^ 



.Voon in connexion unth Tra.^t ofif^.^. 



^SZ 



00 

+ 



y» 


VO 


M 




6 


6 


+ •^ 


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■♦- 



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00 

I 



P fO o 

w *^ ;* 



S 




I + 



P 

o 



j;* P ox ^ ^ j^ 

+ ' I + + + ; o o . ^ ^ 



o o 

1 1 



p f> <> lo 

** O A^ • 

' ' I 7 




to 



^1 






I 



I + 



S- 2 
I I 



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r P 
I + 



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O o 

+ + 






+ + 



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r P 
I I 



8 8 
+ ^ 



^ p p r» p N 
' ' I I I ; 



p p 
+ + 



o 



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+ + 



»^ 00 



o\ 



t2 ft, 



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On 



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=2 



252 Capt, Tupman^ Corredicyiis to N.A, Tlaces of XX3 






Xi . 

SL-^ so »^ ^n 

►*• J oD ro to ro 

p* • . . 

Ill 



00 



?5 



I I I 



• • • -^ 

N M »^ M 

I I I I 



9 • ^ 

I '1 *l I *l "1 '1 



• 


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• 





6 


6 


9 


1 




+ 


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^ 


& 


* 
VO 


%, 


CO 



I I I I 



to M t^ M M P >P 



00 



/ d 

T> u^ NO >0 »^ r^ t>» >0 

S'g 



i2««^ r^ r^ 9 ^ »« v^ 
I I I I I I I 



J 



rf w O O so CO 00 

u • • • • • • 

-,•» "^ O -< »- W M 

g + I I I I 



'1 *I I '1 '1 I 



O M - 00 
|!Z5 + + I 



CO ^ VO VO 

• • • • 

« o *^ w 
III! 



I I I I I I *l 



OS p 

+ + 



P 

CO 






Q Op fl r*. 

»;Pl^5 in sb u^ 

•5^* + + + 

s 

t^*«5 s? [: (ff <? <g 

ft* •••••• 

" I I I I I I 



• 

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a 



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o 
O 



p 

NO 
1 


ro 

• 

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1 


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1 




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1 


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1 


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1 


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CO to CO M (^ (i| 
i i I I I I 



»o N ** o 5 3 

VO VO »0 »0 Jo »?» 

• . . 

I I t i I I 



u-> M ^ 10 ro 

• • • • • • 

CO ^ ^ ^ ^ 

I I I I I 



VO CO OS to M 00 

vp \o tn 10 wi ^ 

I I I I '1 '1 



• • 

« o 
+ + 



6 
I 



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CO CO ^ 

I I I 



10 



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* 
CO 



r*. so VO VO w^ to 

• • • • • , 

I i I I I I I 



^5 

o a 

5 



VO 


SO 


r^ 00 


OS 





*m 


« 


N 


N W 


M 


CO 


CO 



»- « CO ^ to so «s. 



Mkrcb 1877. Mom in eomuetion with TrantU of 1874. 



»SS 



+ 



CO 
I 



ft 

M 
I 



eo 


• 


■ 




c^ 


fO 


M 


*N 





M •* 


foi« 


b 


1 


+ 


1 


+ 1 


1 + 


+ 



m^ 


»^ 


9^ 


9m 





M 


•« 


b 


b 





• 

ro 


^ ^0 


• 




1 


+ 


+ 


1 


1 1 


•«- 


1 



P gv -I 
+ + + 



« b o 

+ + I 



p 


• 


-^ 


k« 


9m 


w 


+ 


+ 


1 



00 

o 



9^ 
in 

I 



2> ^ 
• • 

+ I 



P 
I 



+ 






%r\ 



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00 



+ I 



O »• O M 



i I 



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+ 


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d 


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•-• i-» w 



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+ 



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I I 



r P 
+ + 



^0 



O 



o 

I 






po ^ m NO r>i ON ►- 

W N M M M (>4 






* P 



1 



256 OapL Tupman^ Oorrectiana to N.A, Places of xxxm. % 



I. 



O 



^0 
O 



o 

+ 



>o 



l(«^ 



5-§'» « 6 w 

+ I I 



^^ 



I 



O M O O M N O 
I •!• + I I I + 






r^ u-> »n 
i* >• w 
+ I I 



to 

I 



b 

r 



6 



o 

I 



6 



ro 


^ 


fO 


m 





• 


b 


• 


b 


b 


1 


1 


+ 


1 





+ I 



I 



g 

1 



1 



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P O 



•5§ 



o^ 



.a' 
o 

(3 

I 



+ ♦ 



I 



80 ^0 

I + 



8^^ 8^^ ? 8 

• • • • • * 

I I + I + 



\0 CO M 

W i-i w 

• • • 

I I I 



+ + 



9 

1 



+ 






o 

■ 

+ 



8 



O 



CO 



O 






W fO^»OvO »^0O OvO « C0mt>»0^"* 



•- CO "^ •*% 



09 ej 






: £ 



arch 1877. Moon in eonneciion with Traiisii of 1874. 255 



+ 



7*- 

I 



ft 

M 
I 



7 



• 

+ 



• • • • • • 

I +1 I + + 



b b o fo 
I + + I 



o o r *^ 

^ \0 f** fm 



^ 9" r* 

^ mm in 

+ + + 



« b o 

+ + I 






CI 


-^ 


00 

■ 


• 
mm 


Pm 


W 





+ 


+ 


1 


+ 



ir% 

I 



2> ? 
+ I 



P 
I 



+ 



+ 



m 



O 



00 



• • 

+ I 



S3 *^ S" '-' 

o »^ O M 



i I 



I 



I 



• 


• 


• 


8 


Pm 


mm 
mm 

m 


mm M 
• • 


mm 


VO 

mm 
• 


• 


mm 



mm 



00 

mm 


+ 


1 


1 


1 


1 


1 


+ 1 


+ 


1 


+ 


+ 


1 


• 
1 



r P 
+ + 



^0 



I 



O 

I 



--««*2'?:?j?'S2>8 s a 5" ;rj?"8&8'- 



I 



I 



*»•««» 

*•••»•»•» 



- o 



256 Oapt Tupman^ Oorrectiana to N.A, Placet of izzni. 5. 



O 



^0 

o 



o 

+ 



to 

I 



I 



o 

I 



fO 



CO 

6 

+ 






y> 


• 


^4 


* >o 


^ 


m 


m 00 


00 


t^ 


»n 


• 


CI 





M 


b M 


b 


b 


«< «« 


b 


»« 


M 


M 


+ 


1 


1 


1 + 


+ 


1 


1 1 


+ 


+ 


1 


1 



o 

I 



o 

+ 



*o 


^ 


fO 


m 





m 

»4 


b 


• 

>i4 


b 


b 


1 


1 


+ 


1 





I 



r 



+ I 



I 



+ ♦ 



1(1 



"S 



«> 

«, 




Ov 



O 



^0 

I 



S 



^0 



I + 



8^? g^ ^ ? 8 

■ • • • • * 

I I + I + 



\0 CO M 

w •• w 

• • • 

I I I 



CO >0 

+ + 



"8 

I 



? 


p 


? 


• 


CO 

■ 


^ 


-1- 


+ 




+ 


+ 


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+ 



W CO 



09 ej 



'♦■ »0 vO »^ 00 Ov O 

ta k4 M •-• »« ki* M 



M CO m t>» o^ •* 

M M N N M CO 



i« CO '^ »r% 






ICarch 1877. Moon in eonneciion with Transit of 1874. 



257 



u> 


7^ 


P 


M 


M 


>o 


^ 


CO 


1 


1 


1 


1 



fO»n oop 



to o ^ *>• 

•- o •* o 



vO ^ fO w^ >o 
+ + + I f 



• • . « 
O *-• o VO 

+ I I 



V3 

I 



i 1 



»o 

o 
I 



9 
I 



+ + I 



8> 



CO 



CO 



CI 



00 



S" 



^9 3" = 

• « " ■ 

+ 1+1 



O 'd- 



8^ 
I 



P 



o 







"? 


5 


^ CO Q 
•- CO ?) 


1 + 


1 


+ 


1 


+ -I- 1 



O «p Q o* 

M O N M 

• • • • 

+ + I + 



P 



^ 



00 



-21:12 2' g aa;rJf'85"88'8,?.-*222? 



,0 



258 Oapt Tupman^ Corrections etc. 



9 



■i 

O 



i. 



00^ ^ow 00 •* 

mm *m O O O O 

I + I + I I 



o 



P 

3 43-9 

I gl T + 1 + - I « + 

ll 



:S5 



I I + I 



1 

OQ 



+ + + + 



i 



■*3 



I- ? 8 = 8 2 IT ? 

I ; 1 + 111 + 



"S m 'rob '^^ 5 VP *^ 

I Q^ » • » • • • • 

+ 1 +111 I 






O 



52 I I + I + III 



%l 

fli2« r P r P 

+ + + + 



I' 



iT^r:^ 2^sa«2'N^ 



00 



March 1877. Senor Arcmiisy Obs. of Jupiter* s Satellites, 25$ 

On the Visibility of the Unilluminafed Portuyn of the Dish of 

Venus, "By Senor A. T. Arcimis. 

I had only one favourable opportunity of observing this 
phenomenon in the afternoon of June 19, 1876 ; on the previous 
and following days the sky was overcast towards the West, and 
the prevailing high wind caused considerable vibration of the 
telescope. 

At 7^ 15" the Sun being slightly obscured by clouds, I could 
Bee the planet with the naked eye ; the finder enabled me to 
distinguish perfectly the shape and direction of the crescent. It 
presented, when viewed through the telescope provided with an 
eye>piece of 92 diameters, a most beautiful aspect, although it 
was very difficult to focus, and the image almost invariably was 
irisated. The concave portion appeared as a broken or undula- 
ting line, somewhat similar to the Moon's, and no illuminated or 
'bright cusps were visible on the dark portion. 

The two horns were easily distinguishable. They were un- 
equal, the northern being the sharpest. Close to the southern 
extremity an excavation or indentation of an almost black colour 
was perceptible. I could not discard the idea that the body under 
observation was a partially illuminated sphere ; and this appearance 
became more marked when I employed a very faint red modifier. 
The phenomenon of irradiation seemed to me more striking than 
the Moon's ; that is to say, the bright portion appeared very 
considerably larger than the dark one. 

I had considerable difficulty in perceiving the secondary 
light, but I succeeded in doing so by employing the well-known 
device of not sighting it directly, so that the light might impinge on 
a more impressionable point of the retina. Its colour, to my sight, 
was greyish, or somewhat violaceous, and extremely faint. It 
will be well to bear in mind that this colour might be due to a 
cfeficient achromatic condition of the telescope. 

At 7** 30™ both horns appeared to be equal, and from that 
iHoment the sky was overcast, and I have since had no further 
O£*portunity of observing the planet. 

Cadifff 
X876, December 30. 



^Jieitometia of Japltor^s Satellites observed at Cadiz, By Seiior 

A. T. Arcimis. 

The observations were made with a 4-inch Secretan Refractor 

* d a 92-power eye-piece. The hour of the clock was deter- 

ined by equal altitudes of the Sun or stars, taken with the 

^tant and the artificial horizon. The ephemerides are from 

« Nautical Almanac of San Fernando Observatory; the 

K^ographical co-ordinates of my Observatory are : — 

Lat. N. =36° 31' 52"-8 

Long. W. OrecDwich = o'' 25'" 11 ••7 



26o Senor Arcimis^ Ohs, of Jupiter^ 9 SaieiUUes. XXXTI 



Date of 
Observation. 


1 


fi4 


Mean Solar 
Time of 
Obaerration. 


Mean Solar 

Time from 

N.A. 


Diff. 


RemazfcB. 


1876. 




h m 8 


h m • 


m • 




April 24 


I 


D 


894 


892 


-0 2 


Moon abwnt 
sky. 


», 25 


11 


D 


14 43 39 


14 43 40 


+ I 


da d( 


., 26 


TTT 


D 


II 16 55 


II 16 52 


-0 3 


Good obaenrat 


„ 26 


ni 


R 


12 58 43 


12 58 35 


-0 8 


do. 


May I 


I 


D 


10 2 53 


10 2 51 


—0 2 


do. 


» 3 


in 


D 


15 15 I 


15 14 53 


-0 8 


Bad dAfinitioii. 


» 8 


I 


D 


II 56 12 


II 56 44 


-0 32 


Clear sky ;Moc 
near planet 
lite very tie 
I lost it lom 


H 20 


n 


R 


14 16 30 


14 16 26 


-0 4 


Gt>od obeerrat 


H 24 


I 


R 


12 21 7 


12 21 I 


-0 6 


do. 


JuDe I 


ni 


R 


8 51 3 


8 51 12 


+0 9 


Bright Moon. 


,. 7 


IT 


R 


8 47 40 


8 46 46 


-0 54 


Bright Moon 
sky. 


„ 8 


III 


D 


II 7 28 


II 5 40 


-I 48 


Qoodobservat 


.. 8 


III 


R 


12 48 17 


12 50 3 


+ 1 46 


do. 


». 9 


I 


R 


10 38 19 


10 38 5 


—0 14 


GK>od obs. ; cl< 


M 16 


I 


R 


12 32 21 


12 32 28 


+ 7 


do. 


.. 25 


I 


R 


8 57 29 


8 55 33 


-I 56 


Bad obt. ; 
wind. 


Julj 2 


I 


R 


10 50 23 


10 50 6 


-0 17 


Good obs. ; 
near Moon. 


», 14 


III 


D 


not obs. 


6 59 33 






,. 14 


111 


R 


8 49 33 


8 46 57 


-236 


Strong wind; 1 
vibrates. 


„ 16 


I 


R 


14 37 48 


14 39 23 


+ 1 35 


do 


„ 16 


11 


R 


II II 52 


" 9 35 


-2 17 


do. 


„ 18 


1 


R 


9 14 24 


9 8 5 


-6 19 


Clear sky. 


» 25 


I 


R 


II I 6 


II 2 48 


-1- 1 42 


Cloudy ; plan 



horizon. 

Aug. lO II R 8 23 o 8 21 48 -1 12 Very strong w 

observation. 

„ 10 I R 9 21 17 9 20 58 -o 19 do. d< 

,,26 I R 7 39 16 7 39 II -05 Good observ. 

present. 

„ 26 m D 65359 65321 -038 Good obs. ;tw 

„ 26 III R 8 45 42 8 45 9 -o 33 Good observ. 

present. 



March 1877. 



Senor Arcimh^ Occultations, 



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262 Mr. Penrose, Lunar Eclipse of Feb. 27, 1S77. xxrm- 

The OccuUatiou of Begulus, February 26, 1877. 
By F. C. Penrose, Esq. 

The occnltation of Regulus, Feb. 26, 1877, was observed be 

h m B 
Disappearance 12 46 14*8 



Reappearance 13 51 



7 la.M.T. 



Two observers watched for the disappearance ; one wW 
2:|.inch 0. G., the other with a sj-inch 0. G. The clouds n 
sufficiently dense to obscure the star in the 2^ -inch before 
occnltation, but it was distinctly seen in the 5^. inch on the d 
limb. At the reappearance the sky was perfectly clear, and 
star was seen as a bright indent upon the limb of the Moon. 

ColebyfielJ, Wimbledon. 

Latitude 51® 24' 58*. 
Longitude o* o" 55^1 5- 

Total EcUi}se of the Moon, February 27, 1877. 
By F. C. Penrose, Esq. 

I offer a drawing made of the Total Eclipse of the Mooi 
the 27th nlto., at the phase of reappearance of the sunlight, 
could not have failed to be remarked during totality, how ^ 
much brighter the northern and southern parts of ihe Mo< 
limb were than the eastern and western parts; presuma 
arising from some interference with the light refracted throi 
tho Earth's atmosphere, from a greater prevalence of clouds in 
equatoreal regions than at the two poles. Some amoonl 
specular reflection, at very flat angles, from the northern 1 
southern ice, may have also aided in producing this effect. 

With respect to the general phenomenon of the total lu 
eclipse, I would observe that, although no value appears in wo 
on Navigation to be placed on this phenomenon for the del 
mination of longitude at sea, although I admit that this wo 
be perfectly reasonable in the case of a partial eclipse ; ] 
when the eclipse is total, it seems quite capable of givin| 
useful result. The two phases of the beginning and end 
totality should be observed when practicable, and the mean ial 
By combining these observations in the total lunar eclips< 
July 12, 1870, I obtained a G.M.T. differing from the predict 
in the Nautical Almanac by 39', and from the eclipse 
last February by 29% both being later than the predicti 
There would bo less difference than might be supposed in 
use of smaller telescopes ; for I found that simultaneous nnai* 
eye observations of both phases made on the last occasion did 
differ by many seconds. This could, after a little study, be alloi 
for ; and probably, as far as the observation is concerned, the ei 
need not exceed 15 or 20 seconds. The errors of the tal 



liardi 1877. If. de Oasparia, On Kepler^s Problem, 263 

would of course be shared by this with any other lunar method. 
The times I noted were, 

h m B 



Totality commenced 6 28 13 
Totality ended 8 



^^Ig.m.t. 

15) 



The colour seen upon the Moon on this occasion, and especially 
the remarkable bluish hue which spread over the lunar regions 
preceding the reappearance of the sunlight, could not fail strongly 
to impress upon the mind the wish to realise in imagination the 
effect that would be seen from the Moon of the prismatic colours 
surrounding our planet, with the Sun's corona in the background 
and with Venus not far distant. 



Total EcUpse of the Moon, February 27, 1877. 
By the Rev. S. J. Perry. 

The night was cloudless, but there was a sharp frost, which 
**>Ade the air unsteady. The Moon rose partially eclipsed. Using 
* Power of about 100 with an 8-inch achromatic, the following 
^^^^tacts were observed : — 

h m B 
Commencement of Totality 6 27 245 G.M.T. 

End of Totality 8 4 8*5 

Last contact with Shadow 9 o 6*0 

^ The time was taken with a Frodsham chronometer, compared 

the eclipse with the standard sidereal clock ; and clock 
were observed. 

^ The darkness of that portion of the penumbra which was in 
^2^^**® proximity to the umbra was so great, that the last contact 
^^^ difficult to observe. 

1^ Several reappearances of occulted stars were seen during 
^^"^ydity, and misht have been well observed. 

The thin circle of light on the Moon's limb was in such 
contrast with the cloudy dull brick-red shading of the 
, that to many persons it seemed as if the Moon was nob 
^mpletely immersed in the Earth's shadow. 

-^Stamfkurst Ohtervatory^ 
1877, February 28. 




On Kepler's Problem. "By M. A. de Gasparis. 

{Translation.) 

The numerical solution of the equation M = E— e" sin E may 
useful, especially for the new planets, for comets of elliptic 
^^^^t, and for the satellites of double stars, the number of which 

X 



k 



264 M, de Oasparia^ On Keplei^B Frohlem, XjMl ^ 

is always increasinfr. I here reproduce a soluiion, verTikUMri 
simpUfiid, which, p^ceedingby direct opeiations, gi;^ towitlA 
a few seconds the value of E. 

I assume E = M+n. 10°, and we then have by substitutioii 

rio°Y' 
ni^ = eBin(M + n.ioO) (t) 

or, if we please, 

/joy/ 

lOfi^^^ = cBin(M+io».i®) («) 

The unknown quantity is here n, and we know that ii 
integer part is less than 6. For a first step I employ logarithms "^ 
three places of decimals, for the second step to five places. Mon 

over log ^ ^^; = 9*241 8774, and therefore log ^^77- = 8*24i87| 

This being so, 

1° I write in a line the logarithms of i, 2, 3, 4, 5, 6. 

2^ Below these the logarithm of ^ /^ , and I take tl 

sums. 

This operation is common to all the examples whk 
present themselves. 

3° On another line, respectively below the preceding nombea 
I write (six times) loge. 

4° Below the loge's, I write the log sin (M+i,io**)^ L* 
sin (M + 2.io^;. . . log sin (M + 6. to°) ; and I take the sums. 

We have at sight the limits of the integer part of n^ and tsi 
tenths are obtained by a simple proportion. 

Suppose, for example, M = 27° 15' 7"'42, log e = 9*92315^ 
we proceed as follows : — 

I 234 5 € 

log n O'ooo 0*301 0*477 0*602 0*699 ^5 

1^ -on 9*242 9242 9*242 9*242 9*242 9*^ 



R" 



9*242 9*543 9*719 9844 9*941 <rc 



log* 9*923 9923 9923 9*923 9*923. 9"^ 

logsin (M + n.io°) 9782 9*866 9925 9*965 9989 0-0 



9705 9*789 9848 9*888 9*912 9-9 

Therefore n is between 4 and 5. The lower sum of the vertic 
line 4 is greater than the upper sum by 44 ; on the line 5 it 

less by 29 : therefore n = 4 + — 4i-_ = 4*6. We have consequent 



Kaich 1877. Tfof, J^ 5. BoXi^ (M a Transformation etc. 265 

Bss 27* 15' + 46° x= 73** 15'. Since io» = 46, I employ in the 
noond oBse the equation (2) as follows : — 

io« 1*65321 1*66276 1*67210 



8*24188 



8*24188 



8*24188 





9*89509 


y%^ 


Q'PaS'S 


logBm(M+ioii.i<*) 


9^7882 




9*90197 


Bore ion ss j.c 4 


688 



9*90464 
9*92315 

9*98117 

990432 



9-91398 

9*92315 
998338 

990653 



^^ . ^gg_^^^ = 45*956; but 45°-956=45*'S7' 22". 

Therefore B = 27** 15' 7"-4+45** 57' 2i"*6 ; or, E = 73° 12' 29'', 
A ^alxie ezaci to within a few seconds. 

The definitive coirection AE, may be obtained from 



AE 



I— «008E~" 



^"^plti, M, 7, 1877. 



S<>*e on a TransfomuUion of Lagrange'a EquaHcna of Motuni in 
OmerdUsed Coordifudes^ which is convenient in Physical 
Astronomy. By Robert S. Ball, LL-D., F.B.S., Royal 
Astronomer of Ireland. 

^ I can hardly suppose that the following Note contains any- 
^^^ which has not already been published ; but as I liavo not 
^^ with this transformation in my reading, nor conversed with 
^JTone who is acquainted with it, I am led to believe that, even 
^ itbe not new, it is ceitainly not so well known as its convenience 
vieiTes. 

lagranffe's Equations of Motion in Generalised Coordinates 
^notjin tneir usual form, particularly well adapted for Physical 
^*tamomy. In a problem in Physical Astronomy, what wo want 
*y leam is the relative coordinates of a system, while its ahsolute 
[''wition in space does not concern ns. Lagrange's equations^ 
^'^eyer, involve both the relative and the absolute coordinates, 
•od we are obliged to remove the latter by elimination. It is the 
J^ject of this Note to point out a very simple transformation of 
^[Wnge's equations which obviates the inconvenience of having 
^ perform the elimination. This advantage is gained without 
y^^Wcting from the simplicity and directness which render 
^[niige's equations such exquisite instruments of analysis. 

X 2 



266 ^rof, U, 8. Ball, On a Transformation xxxm. 5, 

If g be one of the generalised coordinates, and T and Y be the 
kinetic and potential energies of the system, then Lagrange's 
equations have the form 

dt \d^) dq '^ dq* 

V depends solely upon the relative coordinates of the system. 
It is therefore only the function T which requires to be parged 
from the three objectionable quantities. This is effected hf 
simply replacing T by a different function, which we shall denote 
by T'. 

We proceed to show that this substitution is allowable, and 
that it answers the end for which it is intended. 

Let J? I, j?2> Vz ^^ *'^® rectangular coordinates of the centre of 
inertia P of one of the bodies with reference to axes fixed in space. 
Let the relative generalised coordinates of the system be $1, . . . g.-a. 
When the last-mentioned coordinates and the corresponding 
generalised velocities are known, then everything is known about 
the system except its actual situation in space. What we want 
to obtain is a system of 71— 3 equations in ^1, . . . g^.g) from which 
P\iV%y Pz Are absent. 

I^^ ^1) Viy ^1 be the rectangular coordinates of the centre of 
inertia of one of the masses m| with respect to three rectangular 
axes through P parallel to the fixed axes, then we have 

T - i aw, (Pi+i,)« + ^ a»h (Pa+yir + ^ 3;;i. (A + -^i)« + R«, 

when Rj, is that function of ^i, . . . g^.j and ji, • • • </«_s whicl^:r 
expresses the kinetic energy of the rotations of the bodies of th^^ 
system about their centres of inertia. 
Then we have 

We first form the generalised equations of motion in Lagrangi*— * 
form corresponding to the coordinate |7i : 

dT 
dV 
whence the equation of motion is 



iarcli 1877. of LagrangeU Equatiaiw ofMoHon. 267 

kud two similar eqnaiionB, corresponding to jps and ps. If then 
«) V, 10 be constants with respect to the tune, 

p,Xii, + aw,y, - V aw,, 

We now proceed to form the equations in gi, . . .^n.^. We shall 
ue the letter q as typical of the series. 
If we make 

tben it is easily verified that 

Making this snbstitntion in the equation of motion corre- 
sponding to 9, yiz. 

^ equation becomes 

But thb equation may be greatly simplified, for 






Of, if we 



assume 



we have 



TT ^^1^1 






^^Uis a function of gj, . . . ^r^.si *^^ ^^^ ^^^ contain t or 
^'' • • • kt'tt or jpi, Pj, j?8> whence we may write 



^ ^dX5 . 



368 ^XPf' ^' S. BaU, On a Tramformatum etc. xxxra. 5, 

It fpUowfii that 

dq dq 
du rf«U 



dq dtdq* 



and finally 



(du\ du 
44)- d^ ' °- 



d_ /du\ du 

dt 



B V 1 

T, the 



Similarly it may be shown that 

d_ /dv\ dv 

dt \dq/dq ■ ^ 

d_/dw\ dfo 
dt\di)~dq'"^'' 

and therefore the equation of motion redooes to 

d /dT\_crr dV 
dt\dq) dq dq' 

By slightly altering the method of expressing the function 
final result may be stated in the following theorem : — 

Let y denote the potential energy of a system of attracting 
bodies. 

Let T^ denote the sum of the kinetic energies of the rota- 
tions of each body of the system about its centre of inertia 
added to 

2 ^[1.2], 

25w, •• ■• 

where the symbol [i, 2] denotes the square of the relatiye 
Telocity of the centres of inertia of the masses m| and mt, and 
the summation includes every pair of the bodies of the system. 

Let (7i, . . Qn-z be n— 3 generalised coordinates adequate t<a 
specify everything about the position and aspect of the sjate: 
at a given epoch, except its actual situation in space, then th 
n— 3 equations which will determine the motion are 

d /dT^^dT' _dV 
dt\dqj dq^^ dq,* 



dt \dqn-J dq^^ 



d9 



H-i 



In these equations the three objectionable coordinates do 
not appear, and thus the required elimination has been effected. 



March 1877. Trof, Oayley^ Additiw. 369 

Addition hy Prof, Oayley, 

The formidsa may be established in a somewhat different 
way, as follows : — 

Oonaider the masses Mi, M^, , . . 

Let Xi, Yi, Zi be the coordinates (in reference to a fixed 
origin and axes) of the C. G. of M^ ; 

^1* Vu ^1 ^6 coordinates (in reference to a parallel set of 
axes tlurongh the 0. G. of M|) of an element mi of the mass 
M], and similarly for the masses Mj, . . . ; the coordinates 
(X|, Yi, Z|), (X2, Y2, Z2), . . . all belonging to the same origin 
and axes ; 

And let ii &o, denote the derived functions -j-^ &o. 

at 

We have 

or since StniWi = o &o., and therefore also S miii = o &o,, tbis is 
T- |M,C&,'+t,'+2;,«) +si«t,(i,«+^,«+*,«) 

Write 11, V, to for the coordinates of the G. G. of the whole 
system, then 

Ml Xi + Mt X,+ • • =5 (Ml + Mf • •) ^» 

M,Yj + M,Y,+ ..-(M| + M,..)v, 

M,Z, +M,Z,+ .. = (M, + M,")«;; 
and thence 

M,ii + M,i,+ ..-(Mj + M,..)*, 

M,*i + M,Y,+ ..-(Mi + M,..)v, 

M,4,+M,2,+ .. =(Mj + Ma..)t&; 
and thence 

T--(Mi + M,+ ..)(tt*+«"+tt») 

+ S i «,(*,« +y,'+V) 



\ 



368 ^''^,^' ^' ^' BaJH^ On a Trafntfcrmatum etc. xxxm. 

It follows that 

dq dq 
du d^V 



dq dtdq* 



and finally 



d^{du\^du 

di Kdi) dq"^' 



Similarly it may be shown that 

d_/dv\ dv 

dt Kdq/dq " ^ 

d /dw\ dtp 
dt\di)''dq'"^'' 

and therefore the eqnation of motion reduces to 



d_(^\^^_dV 
dt\dj[/ dq^ dq' 

Bv slightly altering the method of expressing the fanotiot: 
T , the final result may be stated in the following theorem : — 

Let y denote the potential energy of a systm of attracting 
bodies. 

Let T^ denote the sum of the kinetic energies of the lotai 
tions of each body of the system about its centre of inertifl 
added to 

^—=-^ [l, 2], 

where the symbol [i, 2] denotes the square of the relativi 
velocity of the centres of inertia of the masses m^ and rOf^ ani 
the summation includes every pair of the bodies of the system. 
Let q\, ' » q^-i be n— 3 generalised coordinates adequate ti 
specify everyUiing about the position and aspect of the systen 
at a given epoch, except its actual situation in space, then th* 
ti — 3 equations which will determine the motion are 

d /dT\_dT ^ _dy 
dt\dqj dq^ "* dq^* 



d / dT \_ dT 
dt Vi.-J rfj»-3 * 



dV 



dq 



it-3 



Li these equations the three objectionable coordinates dc 
not appear, and thus the required elimination has been effected. 



Marcli 1877. Dr. Boysion'Pigott, On Photogra^Mig etc. 271 

And this being so, then, if g now denotes any one of the 6n— 3 
oooxdinates, each of the remaining equations assumes the form 

dt' di dq dq* 

Tiz., we have thus 6n~3 equations for the relative motion of the 
bodies of the system. 



On Photographing Solar Transits by the use of the " Starlit 
Transit Eye-piece*^ formerly described; and otJier methods. 
By Dr. Boyston-Pigott, M.A., F.B.S. 

It may perhaps be recollected that the eye-piece contains a 
ruled micrometer, displaying equidistant parallel lines drawn 
on a silver film with great accuracy. At present the Sun tran. 
sits in a five-feet telescope from line to line in five seconds — a 
second per foot of focal length. 

If the image of thjs Sun in transits be projected on a screen 
of paper, a peculiar phenomenon is observed worth noting. So 
soon as the solar light illuminates the field, the transparent lines 
remain black until the sun flashes across the lines. 

On the instant that the limb makes contact, a bright line is 
Been rapidly lengthening as a brilliant tangent, becoming a 
chord to the disk. 

During the passage of the Sun across the bars, at each 
xunnte change of position the phases of the bars pass through 
9k continual series of varying patterns. 




If now an instantaneous photograph be taken at a known 
instant of time, the measured length of any one of these brilliant 



272 J^r. Eoyston-Pigott^ Chi Photographing XXXTIL 5 ; 

chords, and — still better — ^tho measured leng^ths of several, ma^ 
be employed aocurately to determine the instant the Sun's oentne 
would transit each particular bar. 

Let C be the Sun's centre approaching the brilliant bar BB' 
at the precise mean time M. Let BB' be measured on the screen 
placed at a known fixed distance from the object-glass, so that the 
apparent diameter of the Sun may be assignable on the aoreea: 
so as to compare the length of the bar BB' with the diametoi 
of the Sun. 

Then the time which will elapse before the centre of the Snr 
will transit over BB' is (r being the semi-diameter of the Sun ii 
time, 6 the angle BCA, and ^A being half the length of the htf' 

< = CN = r cos ». 
Also 

. . BN iA 

Then the time of transit of Sun's centre over BB' will be M-|-fl 
If several bars be measured on the photograph, say three 

T, the mean time, = -(/, + ^2 + ^i)» 
or 

T = - • (cos 6, + cos 6, + cos 6,) ; 

and the final result for the time of passage of Sun's centre 
M+T. 

Should some of the bars be to the West and the others to tb 
East, cos 6 will have contrary signs algebraically. 

Or if there are n bars measured, then, according to the usus 
notation, 

T = - 2 (cos e\ 

Now, admitting that the lines are ruled very accurately C 
thing not approached by mechanical arrangement of spider lines^ 
any one of these lines should give the same instant of transit 
because the centre passes each after equal intervals. B 
inspecting the tables of natural sines and tangents, it appeal 
that, up to the first 18 minutes of arc, the tangents and sines ar 

identical up to the th of the radius, and the minute 

10,000,000 

of aro up to the semi-diameter of the Sun are equal within th 



1 87 7* Bciar Transiia by the Stan'lU Trcmsit Eye-piece, 273 
ih of the radius. From this it follows that the 



30,000,000 

:xiieasiirement8 of the bars, if drawn equidistant, for a telescope 
of 100 inches focns will not exhibit a taogential error exceeding 

the th of an inch. At the fall breadth of the image 

10,000 

of the Sun — 32 minutes — the error would be no greater. But as 
the field of yiew would probably not much exceed the semi-dia- 
meter, the tangential error from employing equidistant lines may 
be neelected. 

The difficuliy of ascertaining on the screen the precise 
magnitude of the Sim's semi-diameter ma^ be avoided by using a 
Bcreem at a standard distance from the meal point of the object- 
^laas. And if a single uncemented triplet be used to throw the 
image upon the screen, whose focal lengtli for simplicity is i inch^ 
say at a distance of 10 inches from it, the usual formulas for 
optical foci will give 

III 10 

— +- — -, or t> « — , 
10 V I 9 

^nd the magnifying power on the screen will be 

u 10 

- — 104-— = 9, 
V 9 

BO that^ at the distance of 10 inches from the eye-lens of the 
^^eleecope (with a i-inch triplet), the disk of the Sun will be 

onagnined exkcHj nine times. 

The actual size of the disk of the Sun at the focus of the 

telescope is readily obtained from the equation 

D - F sin », 

F being its focal length and ^ the diameter of the Sun. 

If the focal length be 60 inches, for example, and the Sun's 
^iiameter be 32' 2o'''2, the diameter on the screen will be 



logs 



9F Bin 32' 2o"'2 

log 9 = 0-95424 

+ log 60 = 177815 

.+log32' 2o"-2 « 797334 



inches 



(rejecting the index) 1070573 = 5 078 

By a slight shifting of the screen, the Sim's image for the day 

may be made exactly to correspoud with 5 inches. Should that 

\>e too large a photograph, then a telescope of shorter length can 

be used. At indi^ distance the image will be magnified five 



i 



372 J^r, Eoyston-Pigott, On Photographing SXtnu 5, 

chords, and — still better — the measured lengths of several, may 
be employed aocuratelj to determine the instant the Sun's centar^ 
would transit each particular bar. 

Let C be the Sun's centre approaching the brilliant bar BB' 
at the precise mean time M. Let BB' be measured on the soreeii 
placed at a known fixed distance from the object-glass, so that the 
apparent diameter of the Sun may be assignable on the screen ; 
so as to compare the length of the bar BB' with the diameter 
of the Sun. 

Then the time which will elapse before the centre of the R"« 
will transit oyer BB' is (r being the semi- diameter of the Sxin h^^ 
time, d the angle BC A, and ^A being half the length of the bar]^ 

< = CN = r cos ». 
Also 

Then the time of transit of Sun*s centre over BB' will be M+^ 
If several bars be measured on the photograph, say three 

T, the mean time, = -(/,+/, + <,), 



or 



T = - • (cos 6, + cos 6(4 cos 6,) ; 

and the final result for the time of passage of Sun's centre ia 
M+T. 

Should some of the bars be to the West and the others to the 
East, cos 6 will have contrary signs algebraically. 

Or if there are n bars measured, then, according to the usual 
notation, 

T « - 2 (cos 0). 
n 

Now, admitting that the lines are ruled very accurately (a 
thing not approached by mechanical arrangement of spider lines), 
any one of these lines should give the same instant of transit, 
because the centre passes each after equal intervals. By 
inspecting the tables of natural sines and tangents, it appears 
that, up to the first 18 minutes of arc, the tangents and sines are 

identical up to the th of the radius, and the minutes 

10,000,000 

of arc up to the semi-diameter of the Sun are equal within the 



March 1877. of Lagrange^ 8 Equationa ofMoUon. 267 

and two siimlar equations, corresponding to p2 and p^. If then 
^, V, whe constants with respect to the tune, 

^, 2m, + 2772,^1 = w'imi. 

We now proceed to form the equations in gi, . . .9^-9* ^^ shall 
nse the letter q as typical of the series. 
If we make 

then it is easily verified that 

Uaking this substitution in the equation of motion corre- 
sponding to q, viz. 

the equation becomes 

d /dr\_dT' _rfV 

fiat this equation may be greatly simplified, for 

d i 27w,»,\ 



or, if we assume 



we have 



TT ^^1^1 






but U is a function of gj, . . . ^r^.si and does not contain i or 
2i, • . • ^»-8» or j?i, Pj, jp„ whence we may write 



274 L Vr. Boystori'Pigotty On Photographing xxxvn. 5, 

times, iust one time less than the number of inches of the screen 
from tne lens, as seen from the formula 



I I 
for then 



5+«-'' 



V 



d-f 



and the diameter of the Sun will be 2' 82 1 inches. At 3 inches it 
will be magnified twice, and show a disk of diameter 1*128 
inches. This very useful law for a i-inch lens gives at once the 
magnifyinflr power at any distance ; say 30 inches distance from 
the lenS| uie image will be 29 times greater than the object in 
its focus. 

Doubtless many methods will suggest themselves for utilis* 
ing the appearance of the brilliant solar bars during observations 
for a transit. Suppose the photograph taken shortly before the 
time of central transit, so that the whole system of equidistant 
parallel bars are illuminated : the most favourable bar will 
evidently give the most exact position of the Sun's centre and 
the time of transit, viz. the bar or bars which give the smallest 
chords ; for here they increase most rapidly. 

Should the observer calculate the times from several bars^ 
and take the mean of each, I presume this mean would scaroelj 
differ from that obtained f]X)m the most fiftvourable bar. 

In photographing, the effect of obliquity of vision or parallax 
by displacement of ^e eye from the true optical axis is avoided. 
Also another error, irradiation, will so nearly affect botib the 
disk of the Sun and the extremities of the briUiant bars as to 
lessen this source of error, which for Vetius is about, I beliere, 
half a second, and probably not much more for the Sun. Now 
half a second will not be much on the screen, and at each end of 
the bar this will make a whole second ; and on a screen placed 
at 9 inches, this will with the telescope in question be one four- 
hundredth of an inch, and for a disk 2 inches in diameter it wiU be 
reduced to a thousandth. I do not therefore apprehend irradiation 
will be a serious error, if neglected. But it will be measurable 
by comparing a maximum bar with the Sun's calculated diameter 
on the screen. 

In the case where a second photograph is taken after central 
transit) there will probably be great choice of verification bar& 
This method does not necessarily require the Sun-picture to be 
taken at the instant of transit. 

But if such a system were preferred, a thin plate of glass 
placed at right angles to the axis, between the lens and the 
screen, and close behind the former, would both transmit ibe 
picture and reflect it to the observer in parallel rays by a 
suitable lens. The observer could then, by a spring, flash tbe 
phc>togn^h at the most favourable instant. 

Su[^>osing several bars are then chosen, avoiding those wbicii 



March 1877. Solar TSransUs by the Starlit TraH&it Eye-piece, 275 

are formed nearij equal to the diameter of the San, the determi- 
nation of the diatanoe of the Son's centre from each of the chosen 
bars will be mach &cilitated by using the natural cosines of d 
after determining the yalne of from the equation 



sin 



r 



bilf a bar 
rad. of SuD 



The foregoing equation 



T = - 2 (com e) 
n 

will then give the time of transit of the Sun's centre, and the 
sign of the result, whether positive or negative, w'ill show whether 
the time of observation is before or after the true transit. 
Moreover, should the first numerical differences not be exactly 
constant between cos Oj, cos 63, cos 63, &c., two things may 
hi^jpen : either the lines are not ruled precisely equidistant, or 
else the measurement of the bars is untrue. Fpr, since 
t = r COB 0, and r is constant, t varies as cos d^ so that cos must 
increase exactly jpanjxu^u with the time the Sun has passed, or 
will reach a given bar. 

After taking the sum of the natural cosines arithmetically, 

the final value of +T = - x sum of the cosines will of course be 

n 

readily found by logarithms. 

Probably sufficient accuracy (as perhaps diminishing the 
effect of irradiation) will be attained by prcfen*ing bars forming 
chords nearly subtending 60°, or equal to the Sun's radius. 

A trigonometrical example may possibly interest some of 
our Fellows, and I therefore beg to submit one. 




the bars 








A| 


^2 


\ 


^4 


+ I8-2 


+ 256 


402 


40 



322 



276 Dr. BoyBtcmr-PigoUy On Photographing xxicvii. 5, 

be measured ; determine the valae of the times of transit of the 
Son's centre over each bar : (r = 3 2 68) 

* * 2 X 32-68 32*68 

log sin «, = {__ j.'^^J^ } = 9-4447. «i = 16** iC 

log 008 0, s 9*9825 

log r 008 e, = { +9.9825 } " ^'^^^' *' " 31-39 

"''' ^"" 3I68* ^^ "'^ ^*" { - 1-51428 } " ^59293. «« * am 23° 4' 

log COB e, = 9-9638 1 ^ „_o, . ^ ,0.^. 

+ logr- +15143 /'"^7^'' '•= 30-07 

Bin 0, - ^g, log Bin e, - { _ j:3°3J } = 97888, e, - 37-57' 

«, = rco8»,^ +logr= +1-5143 /=Miii. «.= ^5 77 

«^^*'3^'^^S^'^^^={-r5ii3 } = 97867, e,- 37^44' 

* *L +logr= +1-5143 J t t» 4 ^j j^ 



• i> i6-i , . a / 1-2068 1 ^ « o / 

^ ^* = p-68' ^°8 ''° ^* = I - I-5I43 J " ^'^^'^' ^* " ^^ 31' 

log cose,- 99396 -^ _ _ 

log r = + 1-5143 / - ' ^539. ^5 - 28J4 

The bars Aj, A2, A3 lie east of Sun's centre and are negative. 
Times of Son's centre passing the 

•D A A AAA /ifMbeM.T. 

^^ ^« ^ ^« ^* ^* 1 of transit, 

M± -31-39 -30-07 -25-77 2585 2845 

Differences 1-32 4»-30 51-62 2"-6o 

By the microscope the intervals of each can bo accurately 
measored with ease to the 10, 000th of an inch, as also the width 
of the cuts. By a low power, the photograph would probably 
yield the constant of irradiation for the given telescopD, wh ich, 
however, will probably vary with greater or less biilliancy of 
the Son, and states of the atmosphere. 



Marcli 1877. Solar Transita hy the Starlit Transit Eye-piece. 277 

The extremiiy of each bar will be projected outwards by the 
irradiation ; while the breadth of a bar will be determined by 
mixed optical oaaseB, snch as diffraction and interference, as the 
lecnliar darkness of the bright bands before illumination by the 
Inn particularly denotes. Again, tlie known diameter of the 
Sun oomparod with its image wiU be another method for de- 
termining readily this error. 

I offer this method with great diffidence to the Society, 
haying myself no practical knowledge of photography. Nor 
am I able to offer any valuable opinion whether this method of 
silTer-film bars for transits is of any advantage. For myself, I 
have been contented with watching the very beautiful appear- 
ances of the transit of the Sun across these film bars, either pro- 
jected on a screen or directly with a darkened eye- piece. 

The method of direct observation by projection appears to 
hsLve some advantages. The screen can readily be sketched 
with an exact copy of the illuminated bars, and divided into a 
scale of parts ; the observer, at a given tick of the clock, can 
mark with a pencil the precise position of the extremity of a 
given bar. The diameter of the Sun may easily be enlarged to 
a foot. The lens spoken of as a triplet is an extraordinarily 
fine one, by Wray, formed of three glasses cemented to each 
other with balsam, and capable of displaying a very fine image 
of the Sun at 10 inches. 

Shonld the solar heat melt the balsam, Mr. Wray can very 
readily construct these triplets without balsam. And if one of 
the interior surfaces is faintly blued with silver, the glass becomes 
a useful and beautifully defining eyc-picce, thoagh of small field. 
A large shade of pasteboard slipped over the object end of the 
telescope greatly improves the splendour and distinctness of the 
projected image of the Sun ; and a number of triinsits across the 
bars, by the commencing flash and length, can be taken with 
great ease and comfort by the observer, the eye being entirely 
saved the heat, glare, and strain usual to the generally adopted 
method of spider lines. But, I again beg to repeat, I feel quite 
incompetent to form any opinion of the real value or utility of 
the methods now described. 

I would add (while correcting the proof) that if the silver 
film be just the suflicient thickness or opacity to permit the 
outline of the limb of the Sun to l>o photographed, it is pro- 
bable that nearly the whole of the irradiation of the limb may 
thus be destroyed, leaving that of the extremities of the bars in 
full irradiatory display. 

The time can also afterwards, by the same translucent bars 
be compared with a star transit. 



Capt. Ahney, On Effed of Sotation etc Xzxm. 5, 



Effect of a Star's Rotation on ila Spectrum. 
By Capt. W. de W. Abnoy. 

Having privately asked oar. Presidant at the last meetiDg if 
he had considered tae effect that wonld be prodaoed by the ro- 
tation of a star on its ^pectrtun, and having received a n^^tive 
ansirer, I have ventored to bnng the snbjeot before the Sooety 
to provoke discnssion if possible. 

The light which radiates from every part of the visible sar&ce 
of the star will fall on the slit of the spectroscope ; hence ft 
separate spectrum dae to every portion of it will be formed. 
The advancing limb — snpposing there is a rotation of the star — 
will oanse the absorption lines to move towards the violet end, 
and the receding limb towards the red end of the speotmm; whilst 
the central portion will canse them to oconpy their normal po- 
sitions, provided there be no motjou of the star in space. 

As an example of whatwoald oocnr, let na snppose the star's 
disk to be divided into three equal pu-ta ; one ot which is ad- 
vancing towards as, another receding at the same rate, and 
the third motionless. If we draw an ezi^^gerated diagram of a 
small part of the spectra given by the light radiating from these 
three snr&ces, we shoald get a resnlt as shown. 



i 



There would be a total broadening of the line, coDsiating of 
a sort of doable pennmbra and a black nncleus. If the displace- 
ment was equal to half of the breadth of the line, the doable 
penambra alone would remain; whilst, if it were eqnal to the 
total breadth of the line, there would be only one penumbra. 
If we suppose the stellar snrface to be equally bright throngh- 
oat, we snoold get a graduated shade forming the penambra ; 
which wonld gradnally melt off into the blacker nncleus which 
woald form Ibe line. I have calculated what the shade would 
bo ; but I have not thought it necessary to bring forward the 
formnlffi to-night. 

It seems, supposing the surface of a qaickly rotating stAr 



March 1877. Mr. Knotty On TJ Oeminontm, 279 

to be in the same condition as the Sun as regards gaseotis 
pressure and temperatare, that no absorption line due to the former 
can be as sharp and distinct as it is when seen in the solar spec- 
tmm. More tlum this, rotation might account for the disappearance 
of some of the finer lines of the spectrum ; and perhaps other 
phenomena observed may be attributable to the same cause. It 
appears also that, other conditions being known, the mean velocity 
of rotation might be calculated, or perhaps even the angular 
velocity. Since Dr. Hugginshas commenced taking photographs 
of the spectra of stars, he may be able to give a thought to these 
points. I am convinced that from a good photograph much 
might be determined. 



Ou the Variahle Star TJ Qeminorvm. By G. Knott, Esq. 

Mr. Hind's curious variable star, IT Oeminorum, has 
reoently passed a maximum^ of which I have obtained the fol- 
lowing pretty complete series of observations : — 



1877 February 16 


h 
II 


m 

40 G.M.T. 


Mag. 
140 


17 


7 


30 


140 


20 


8 


10 


132 


21 


10 


30 


9-8 


23 


8 


45 


9.9 


25 


10 





99 


26 


9 





985 


27 


9 





9-9 


28 


7 





9.9 


March I 


7 


35 


995 


4 


II 


50 


11*2 


5 


10 


30 


117 


6 


9 





123 


8 


8 





137 



The maximum was a rather faint one. The colour of the 
star throughout its apparition was white or blaish white, and on 
February 27 and March 4 was noted as hazy. 



CvekfieU, 
12*77, March 9. 



28o 3fr. Tebhutt, On hi Argus. xxxth. 



Note on the Double Star ^ I. 62. By S. W. Bambam, Esq. 

The place of No. 62 of Sir William Herschers Glass I. u 
given in the Synopsis of his Catalogues {Memoirs of the R.A.B.ym. -^ 
vol. XXXV.) for 1880, as : 

RA. = 20^ 58-8. 
Docl. = +6<* iY'6. 

No measures of distance are recorded ; but the angle was J 
measured twice, 234°'8 in 1783-4, and 237***i in i8o2'8. In^fl 
the course of a search for the double stars of Herschers Class !.,»* 
not found in Mensurae Micrometricae, this was carefully lookedL.. 
for several times in and near the assigned place, but nothing oi 
the kind could be found ; and I became satisfied that in this, aa 
in many other pairs previously identified, there was a consider- 
able error in the place. It has since occurred to me that this i^ 
probably identical with No. 269 of my Fifth Catalogue of New 
Double Stars {Monthly Notices^ November 1874), there being an 
error of i^ in HerschePs declination. The place of the new pair 
(1880) is :— 

R.A. -20»* 58" 39*. 
Decl. = +7*» 19' 6". 

Baron Dembowski has measured this on three nights, giving a 
mean result (1875*1), P=25i''*o; D = i"-ii. The direct 
motion indicated by the two observations of Herschel would 
make the position-angle about 245** in 1875. As the pair is 
somewhat difficult, a small error in either of the single measures 
would fully account for this slight discrepancy. As similar 
mistakes in declination are not unfrequent in the lists of both 
Herschels, it may be considered as almost beyond doubt that 
these two pairs are identical. A continued advance in the angle 
will settle the question. There remains but one pair not 
yet accounted for of Herschel's Class I. 

Chicago, 
1877, January 23. 



On the Magnitude of rj Argils. By J. Tebbutt, Esq. 

In the Monthly Notices, vol. xxxi., p. 211, was published a 
series of comparisons of 17 Argils made by me, and extending from 
July 1854 to the end of 1870. The following results are to be 
regarded as a continuation of that series, the comparison stars 
being contained in the Catalogue on page 42 of Sir J. llorschers 
Results of Astronomical Observations at the Cajpe of Good Hope, 



Ibroh 1877. Bciar Tranrits by the Bia/rlU Trannt Eye-piece. 273 

! th of the radius. From this it follows that the 

10,000,000 

measurements of the bars, if drawn equidistant, for a telescope 

of 100 inches focns will not exhibit a tangential error exceeding 

the th of an inch. At the full breadth of the imaire 

10,000 ° 

of the Son — 32 minates — the error would be no greater. But as 
the field of yiew would probably not much exceed the semi-dia- 
meter, the tangential error from employing equidistant lines may 
bencttlected. 

The difl^culty of ascertaining on the screen the precise 
magnitade of the Sun's semi-diameter nuw be avoided by using a 
screen at a standard distance from the ^ocal point of the object- 
glass. And if a single uncemented triplet be used to throw the 
unage upon the screen, whose focal length for simplicity is i inch^ 
say at a distance of 10 inches from it, the usual formuka for 
optical foci will give 

III 10 

— +- — ~, or « - — , 
10 v I 9 

and the magnifying power on the screen will be 

u 10 

- — 10-r— = 9, 
V 9 

80 that, at the distance of 10 inches from the eye-lens of the 
telescope (with a i-inch triplet), the disk of the Sun will be 
magnified exactly ntna times. 

The actual size of the disk of the Sun at the focus of the 
telescope is readily obtained from the equation 

D « F sin «, 

F being its focal length and I the diameter of the Sun. 

If the focal length be 60 inches, for example, and the Sun's 
diameter be 32' 2o'''2, the diameter on the screen will be 



log J 



9F siD 32' 20"'2 

log 9 = 095424 

+ log6o = 177815 

. + log 32' 2o"-2 » 7*97334 



inches 



(rejecting the index) 1070573 =* 5 078 

By a slight shifting of the screen, the Sun's image for the day 
may be made exactly to correspond with 5 inches. Should that 
be too large a photograph, then a telescope of shorter length can 
be used« At 6 inches distance the image will be magnified five 



282 Dr, Bohinsony On Befledors and Befrtidon, xxxflL 5« 



On the Relative Spaee^peneirating Power of Reflectors and 
Refractors. By the Rev. T. R. Robinson, D.D. 

I have at last obtained access to the Memoir in the BtiUeHn 
de VAcadimie de St.-Petershourg to which M. Stmve refers me. 

It shows that M. Radan did not make the mistake which ] 
impated to him. I may be ezcnsed for having done so, because 
I did not conceive it possible that one whose authority is so 
high as M. O. Strave's deservedly is conld assert that a 4-feet 
reflector of first rate excellence had scarcely higher power than a 
1 5. inch refractor. 

I was proceeding to show that the observations recorded in 
this Memoir lead to a conclusion the very reverse of M. Strave's, 
when I saw in the MontJdy Notices that Mr. Lassell has so com- 
pletely disposed of the question that such examination of them 
is quite unnecessary. 

But I will give some facts relative to another ^-feet, the 
Grreat Melbourne ' Telescope, which throw some light on the 
question. The American astronomers who observed the TranmL 
of Venus visited Melbourne, and report of that instrument to 
Professor Newcomb that '* its definition is good ; its optical 
power comparable to the 26-inch refractor ; sky is black close 
to large stars instead of the blue light of the secondary spectrum 
shown by the great re&actor ; and that the distant companion of 
Procyon could have been seen close up to Procyon itself." 

It should be mentioned that this speculum has not been 
repolished for several years, though it has been in constant use. 

Armagh^ 
1877, February 8. 



Erratux. 

Vol. rari. p. 361, middle: 

for — I "50 and — 1"-50 read in each case + r'*50. 
viz. the correction to the longitude is 

5i; = + i''-5osin (^ + N-90°). 



Ibrch 1877. Bdlar TransUa by the BtarlU Jh'anmt Eye-^iece, 273 

th of the radius. From this it follows that the 

10,000,000 

measnrexnents of the bars, if drawn equidistant, for a telescope 

of 100 inches focns will not exhibit a tangential error exceeding 

the — - — th of an inch. At the full breadth of the image 
10,000 

of the Sun — 32 minutes — the error would be no greater. But as 
the field of yiew would probably not much exceed the semi-dia- 
meter, the tangential error from employing equidistant lines may 
be ncM^lected. 

The difl&culty of ascertaining on the screen the precise 
magnitade of the Sun's semi-diameter may be avoided by using a 
screen at a standard distance from the ^ocal point of the obj^st- 
fflass. And if a single uncemented triplet be used to throw the 
miage upon the screen, whose focal length for simplicity is i inch^ 
say at a distance of 10 inches from it, the usual formuka for 
optical foci will give 

III 10 

— + - ■ -, or « e — , 
10 V i' 9 

and the magnifying power on the screen will be 

u 10 

- « IO-r~ « 9, 

V 9 

BO that, at the distance of 10 inches from the eye-lens of the 
telescope (with a i-inch triplet), the disk of the Sun will be 
magnified exactly nine times. 

The actual size of the disk of the Sun at the focus of the 
telescope is readily obtained from the equation 

D « F sin «, 

F being its focal length and ^ the diameter of the Sun. 

If the focal length be 60 iDches, for example, and the Sun*s 
diameter be 32' 20''' 2, the diameter on the screen will be 



logs 



9F sin 32' 2o"-2 

log 9 = 095424 

+ log6o = 177815 

.+log32' 2o"-2 » 7*97334 



inches 



(rejecting the index) 1070573 = 5078 

By a slight shifting of the screen, the Sun's image for the day 
may be made exactly to correspond with 5 inches. Should that 
be too large a photograph, then a telescope of shorter length can 
be used. At 6 inches distance the image will be magnified five 



284 Mr. Tod4^ ObserviUicns of the XXXTIL 6, 

reqaired in the adjustment for focus of eye-piece. In taking a 
set of such transit (we generally took 20 on each night), the 
order of observation was alternated ; thus the observer who took 
the last part of one transit observed the first portion of the 
next. 

The value of our relative equation, adopted from all anoh 
observations, was C— H = +o'-o64±o''oo57, Capt Heaviside 
observing in advance of me. 

When near the completion of the reduction of our observa- 
tions of 1875-6 generally, we discovered that we had two difft'Tifft 
equations when observm^ imitation transits, according as the 
motion of the object was from right to left or left to right. 

This led to a re-discussion of aU the observations of ** divided 
transits," arranged in two sets — viz. North Zenith Stars, or those 
moving from right to left, and South Zenith Stars, or those 
moving from left to right — with the following results : — 

8 8 

BjNZStara, C~H « +0*12410*0087 
„ SZ „ C-H « +0*04010*0034 

The application of these eqaations, instead of the one first 
adopted, very much improved our general results. 

On resuming observations this season — 1876-7, we agreed to 
observe every close Zenith star on both sides, i.e. to observe 
it as a North Zienith star over the first 10 wires, and then, 
reversing the eye-piece, to take it as a South star over the last 10 
wires, or vice versa, stars being observed in each order nearly 
equally. 

From 2 1 stars observed by me in this way daring Janiiary, 
I find my equation to be 

8 8 

N-8 - +0*07710*0067 

my observation of North stars, moving from right to lefi, being 
slower than that of South, or left to right moving, stars by 
0**077. I have not yet heard the result of similar observations 
by Gapt. Heaviside. 

Bomh€tyy 
1877, March 19. 



Ohservations of the Phenomena of Jupiter's Satellites at the Obser* 
vatory, Adelaide, and Notes on tlie Physical Appearance of the 
Planet, By Charles Todd, Esq., C.M.G. 

The Astronomer Boyal has received from Charles Todd, Esq., 
of the Observatory, Adelaide, the following communication and 
observations of Jupiter* s Satellites : — 



il 1877. Phenomena of Jupiter* 8 Satellites etc. 285 

** Enclosed I send jon, for the Royal Astronomical Society, 
first oontribntion of observations of Jupiter's Satellites, and 
9^ ^w rough sketches made at the Adelaide Observatory this 
y^smt, I hope to do better at next opposition. 

**In connection with these observations there are two or 
ti^biee things which may be worth mentioning, as I am not sare 
'^^ej have been so well seen before. 

" On one or two occasions when a satellite has been on the 
point of occnltation, it has appeared to be projected on the disk 
of the planet ; or rather, as it appeared independently to my 
assistant (Mr. Bingwood) and myself, as if seen through the 
^ge of the planet, as if the latter were sorronnded by a trans- 
parent atmosphere laden with clonds. I noticed this on two 
^^ocasions, viz. on Angasib 21, at the disappearance of the ist 
B^iellite, when the satellite was distinctly seen on or 
through the edge of the disk for abont 2 minntes before disap- 
pearance — I say through the edge of the disk because the 
satellite was less bright than in a similar position at a transit—^ 
and. aeain at the disappearance of the 2nd satellite on Angnst 
28. Mr. Bingwood also noticed it on Angost 12 and Aagast 19, 
^ occoltation of ist and 3rd satellites. In each instance the 
pl&net was splendidly defined — better than I ever remember to 
'^^ve seen it in England. It was not noticed at any reappearance 
^^lich took place at the eastern or defective limb ; the gibbosity 
^ the planet was, however, quite sensible at reappearance, when 
tihe planet was near quadrature — vide Oc. B. of 3rd satellite on 
^'^^ffist 19, and of 2nd satellite on August 21, when the satellite 
at instant of emergence was sensibly separated from the illumi- 
'^•W edge of the planet. 

" The shadow of the 3rd satellite, when in mid-transit along 
*. Kgh northern parallel on August 30, appeared to me to be 
^"bly oval or flattened at its poles, the definition being all 
Y^ could be desired. On several occasions at ingress of shadow 
^^^ surprised at the marvellous sharpness, the minutest inden- 
^^ion of the limb being at once detected. 

**The phenomena on August 21 were singularly beautiful ; 
p^ 2nd satellite, as it emerged from behind the planet, imme- 
^t«ly passed into the shadow, subsequently reappearing within 
^^^ mmutes of the reappearance of and close to the ist satellite ; 

^ two forming a pretiy coarse double star. 
^ ** The sketches, which were taken for the Jovian Committee 
^ tihe Boyal Astronomical Society, are perhaps not worth much, 
^"ti they are fairly faithful. I was much impressed on some 
°5^ht8 with the sudden and extensive changes in the cloud belts, 
^ though some tremendous storm was in progress on the planet's 
^^■^BKJe, changing the form and dimensions of the cloud belts in 
^^ hour or two, or even less. I hope to do better next year, but 
^^^t^that this humble contribution to Jovian Astronomy may 
^^t be without interest." 

7. 7 



286 



Mr, Todd, Observattofis of the 



ixxvn. 6, 



*J0iilOJ 



i » 



4 

-3 



^ 




e« 



ro 55. tN, 

• • • 

O CO w 

+ + + 



• • • 









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Mr, Todd, Observations of the 



XUJJL 6 



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Afnil 1877. Phmwmena of Jupiter^ s Satellites etc. 



207 



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Mr. Todd^ Obaervations of the 



XXXYII. 6, 



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\pril i877- Phenomena ofJv^pUer's SateUUes etc. 



293 




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XXXVII. 6, 



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29s 



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Mr, Toddj Ohaervatiom of the 



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i877- Phmomena of Jupiisr's Satellites etc. 



297 



to 



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Mr. Todd^ ObservcUions of the 









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OMrOMMMf«f«MM 
C4t«tltlt«tlt«CICI 



O Q O r^t^t^mti^M^N n o Q q ^n t^ \r% ^ ^ 



to eo X 
*n to 



coroto tOtA>*ncO««ww «^» 



.a 00 00 X so NO vo 



fO X 



OS O 
w to 



tn so o so 

^ ^ m w 



ti Ost^ toOsrOsQ^^ Qi 



CO CO '(f '(f « to CO 
OsOsOssOQOSOSOsO t%r<»i^so 






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8 ^ 

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6 *^ 



O 



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(3 



cw. 



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f3 






p4 P w 



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cv. 



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^ •&'& 'A § & R S & ^i a'A 







so 

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o 



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00 osQ •* ti ro^msor^oo o^o »* t« f05h*nso 5 

0000 OvOsOsOsOsOsOsOsOsOsO O O 6 O 90fi 



April 1877. Phenomena ofJwpiier^s Satellites etc. 



299 






^§ 



5^ 

9 

CO 
M 

o 
+ 



00 



CI 



« 






8 ^ « ^ ^ ^ 'g 

• • • • ^ V • 

Ow M ir> vO O Q t^ 

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ttk CO O >0 NO >o VO 

v^ ov en CO CI « N 

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A A 



300 Mr. Todd, Observations eie. XXXYn. 6, 

Noies on Physical Appearance of Planet ^ 187$. 

Jnnc 28, 8.30 P.M. — From about lO*' north latitude to about 20^ to 25® 
south latitude the planet was of a bright salmon colour, raried by streaks and 
patches of cumulus-looking clouds, more especially in the southern portion. 
Over each temperate zone there was a very decided belt of bright camnlns 
cloud, between which and the poles the suHace was of a greyish green or 
olive green colour, mottled with streaks and patches of cloud. The outlines of 
the bright cloud belts were very marked and well defined. — R. 

July 30, 6.35.— On either side of the equator, reaching to latitude 15^ ±, 
the planet was of a pale salmon colour, mottled with small detached cumnlw 
or cirro-cumulus looking clouds and narrow white parallel streaks. The 
southern margin of this band was bounded by a long bank of cumnlns cloud, 
reaching diagonally from latitude 15° or 20° on east limb to latitude 35^ ± 
on west limb, dividing into two branches on west side of the planet*8 polar 
diameter. From the poles to about latitude 60^ the planet was of a dnlL^ 
greyish green, varied with a few bright belts. — T. 

August 29, 7.30.— From about 15® north latitude to 15® south latitude ^ 
the planet was of a salmon colour, over the southern hidf of which 
scattered clouds, between which the salmon coloured ground was risibl 
Between latitude i$° and 2$° north there was a very bright belt of cloi 
having its northern edge very marked and well defined. Between this and 
north pole there were less brilliant cloud belts, overlying a greyish 
ground. Scattered clouds around pole. 

The scattered clouds south of the equator had a remarkable dark bai 
which seemed to bo a rift in the clouds, south of which the clouds had a di 
appearance. In the temperate regions of the southern hemisphere, as also 
the northern, there was the greyish green colour seen between scatter 
clouds ; and round the south polo was of a light greyish colour. 

During this observation it was particularly remarked that in the north, 
hemisphere the north edge of belts and clouds was the most marked and 
defined, which also applied to the south sides of same in the 
hemisphere. — R. 

Oct. 15, 6.42. — Wonderfully beautiful view of planet, definition splendid. 
Over the equatoreal regions, for a space of about 15^ or 20^ on either side of 
the equator, were delicate streaks of cloud, some being knotted like 8¥0&11 
cumulus or cirro-cumulus resting on a background of a deep salmon ^nt. 
Towards the south a bank cumulus, having its hori7x>ntal base towards t^e 
equator, reached across the planet. This bright band, which had the roondiflh 
outline of cumulus, reached nearer to the south pole than usual, or to witl^in 
about 40° of the pole, varied by dark spaces here and there. The north i>ol« 
was of the usual greyish green tint, bounded by a broad bright band over ^^ 
temperate or middle zone. — T. 

The Observatory, Adelaide^ 
1876, Noveinber 30. 





April 1877. Mr. Marihy Bphemeris eio, 301 



Ephemeriajbr PhynecU Observations of Mars, 1877. 

By Mr. A. Marfcli. 

^JJ"Wi Ab^ flf Areograpbical Amount and Position Areooentric 



% 


HwOOIKS 

(T'lAzi*. 


wennn ijong. i i, 
of fbe Centre of <r'i 


aacoae j 
iDiak. 


Jiameter. 


ox ureaccOT iMiecc 
of Illmnination. 


Angle netwe 
Earth and Su 








Diff. 












^BBe 9 


e 





e 





// 


// 





e 


34»-5S 


26977 




-24*19 


12-76 


1*72 


24991 


4309 






70070 












II 


347-85 


25047 


71 


2427 


13*00 


174 


249-80 


4291 


13 


34717 


23118 


2433 


1324 


1*75 


24972 


42*70 








•73 










• 


«5 


34650 


211*91 


•76 


24-38 


13-49 

• 


177 


24965 


42-47 


'7 


345-85 


19267 


•77 


24-41 


13*74 


178 


24959 


42-22 


«9 


34522 


173-44 


2444 


14*00 


1*79 


24955 


4194 








•80 












21 


34460 

• 


154-24 


•82 


24-45 


14-27 


180 


24953 


41*64 




344-00 


135-06 


-84 


24-45 


14-54 


i*8i 


24952 


4I3I 


»5 


343'4a 


11590 


•88 


24-44 


14*82 


r8i 


24953 


4096 


27 


34«-87 


9678 


•90 


2442 


15*11 


182 


249*55 


4058 


^9 


342*33 


77-68 


•93 


2439 


15*40 


1*82 


24959 


40*17 


%i 


341-81 


5861 

* 


roo-97 


-24-35 


15-70 


i-8i 


249-65 


39*74 


3 


341-32 


39-58 

i 


^01*00 


24-30 


16*01 


1-81 


24973 


3927 


5 


340-85 


20-58 


•04 


24-24 


16*33 


i*8o 


24983 


38-77 


7 


34041 


1*62 


•07 


24*18 


16*65 


1-78 


249*95 


3823 


9 


339-99 


342-69 


•12 


24*11 


16-97 


1*77 


250*08 


37-65 

• 


II 

# 


33960 


323-81 


Ami 
•16 


24*03 


17-31 


1-75 


250*24 


37-04 


»3 


339*23 


304-97 


Aw 

•4n 


2395 

• 


17-65 


1*72 


250-42 


3639 


«5 


33889 


28617 


^w 


2368 


17*99 


1*69 


25063 


35-69 


»7 


33857 


267*42 


-25 


2377 


i8*34 


1*65 


250*86 


3496 


«9 


33829 


24872 


•30 


23*68 


18-69 


i*6i 


251*12 


34-18 


ax 


33803 


230-06 


•34 


23-58 


19*05 


1*57 


251*40 


3336 


^3 


33780 


211*46 


40 


2349 


19*41 


1*52 


251*72 


3249 


^S 


337-60 


192*90 


44 
•50 


2339 


19*77 

• 


1-46 


252*08 


31-57 



A A 2 



302 Mr, Marth, Ephemeris for XTJIYJ 



Chwoiwich 


Angle of 


Axeogntphical 




Ajnonnt and Position i 


Noon. 


Position of 


Western Long. J 
ot the Oentro of ^ 


Latitude 


Diameter. 


of Greatest Deftet Ai 


1877. 


<f'8AxiB. 


'sDlak. 




of Qlomination. Hs 








Diff. 
























» 


M 


• 


July 27 


337*43 


17440 


-55 


-23-29 


20-14 


1-40 


25247 


29 


33729 


155-95 


•61 


23-19 


20-50 


1-34 


252-90 


31 


337-18 


13756 


•66 


23-10 


20-87 


1-27 


253-33 


Aug. 2 


33710 


119*22 


701-73 


- 23-01 


21-23 


1*19 


25392 


4 


33705 


100-95 


•78 


22-92 


21-58 


1*11 


25452 


6 


33704 


8273 


-84 


2284 


21-93 


1-03 


25519 


8 


33706 


6457 


• 

-90 


22-76 


22*27 


0-94 


255-95 


10 


337'" 


46-47 


701-96 


22-70 


22-60 


0-86 


25679 


12 


337-19 


28-43 


702-01 


22-63 


22-91 


077 


25777 


14 


337-30 


0-44 


•06 


22-58 


23-21 


0*68 


258-92 


16 


337*44- 


35250 


•10 


22*52 


2349 


0*59 


260*25 


18 


337-61 


334-62 


22-48 


2375 


0*50 


261-82 








•16 










20 


337-81 


31678 


*9T 


22-44 


23-98 


0*42 


263-70 


22 


338-04 


29899 


-24 


22-42 


24-19 


034 


266*01 


24 


33829 


281*23 


•28 


22-40 


24-37 


0*27 


268-92 


26 


33856 


263-51 


•32 


22-39 


24-52 


0-21 


272-70 


28 


33885 


24583 


-34 


22-40 


24-63 


0-15 


27778 


30 


33916 


223-17 


•35 


22-41 


24-71 


o-io 


2849 


Sept. I 


339-48 


210-52 


m 

702-37 


-22-43 


2476 


0*07 


2952 


3 


339-81 


192-89 


-38 


2246 


24-76 


005 


310-5 


5 


340-15 


175-27 


•37 


22-49 


2473 


004 


3314 


7 


34050 


157-64 


-37 


22-54 


24-66 


0x34 


354-2 


9 


34084 


140-01 


-35 


22'6o 


2456 


0-05 


13*2 


II 


341-17 


1 22*36 


-33 


2267 


24-41 


o-o8 


265 


13 


341*50 


104-69 


•30 


22-74 


2423 


012 


35-5 


»5 


341-81 


86*99 


•27 


22-83 


24-02 


o-i6 


41-80 


17 


342-10 


69^ 


•23 


22-92 


2378 


0-21 


4633 



A^pril 1877. PhyHcal Observations of Afar*, 1877. 363 





t Angle of 


Araographical 




Amount and Position 


Axeocentrjc 


Position of 


Western Txmg. J 
of the Centre of ^ 


Latitude 


Diameter. 


of Grmtept Defect 


Angle between 


i's^XxHM, 


'sDisk. 




of lUnmination. 


Barth and 8nn. 








Diff. 












Vfp 



342*38 



51*49 




•19 

•14 
•10 


e 
— 23*02 


2352 


// 
027 



49*74 



12-44 


21 


34263 


33*68 


23*13 


23-22 


034 


5239 


13*97 


^3 


34286 


15-82 


2325 


22-91 


0-41 


54*51 


15*46 


25 


343*06 


357*92 


70204 


23*38 


22*57 


0-49 


56-23 


16*93 


27 


34323 


33996 


701*98 


23*51 


22*22 


0*57 


57*67 


18*37 


29 


343*37 


321*94 


•93 


23*65 


21-85 


0*64 


58-87 


19-76 


tcLi 


343*47 


303*87 


701*88 


-2380 


21-47 


072 


5990 


21*10 


3 


34354 


28575 


• 

•82 


2395 


21-09 


o-8o 


60-78 


22*40 


5 


343-58 


26757 


*75 


24*11 


20-69 


087 


61-54 


23*65 


7 


343*59 


24932 


•70 


24*27 


20*29 


0-94 


62-20 


24-84 


9 


34356 


23IX)2 


64 


24*44 


19*89 


I -01 


62-78 


25-98 


11 


343*49 


212*66 

• 


58 


24-61 


19-49 


1*07 


6328 


27-07 


«3 


343*39 


194*24 


•52 


24*78 


1909 


113 


63*72 


28*11 


'5 


343*26 


17576 


*47 


24-96 


1869 


1*18 


64*11 


29*10 


'7 


343* 10 


157*23 


41 


25*14 


18-29 


1*23 


6444 


3003 


»9 


34290 


138-64 


25-32 


17*90 


1*27 


64*74 


3092 








•36 












21 


34267 


12000 


•31 


25-50 


17*52 


1*31 


64-99 


31-76 


23 


3424" 


101-31 


25*68 


17-14 


135 


65-21 


32-56 








*26 












25 
» 


34213 


8257 


*2I 
•17 
•12 


25-85 


1677 


138 


65-41 


33*31 


27 


341*82 


6378 


26*03 


1640 


1-40 


65*57 


34*01 


'29 

• 


341*49 


44*95 


26'20 


16-04 


1-42 


65*72 


34*68 


31 


341 13 


2607 


26-37 


15-69 


1*44 


6584 


3531 






■ 


08 












N*'»T. 2 


34074 


7*15 


701*04 


-26-53 


15*35 


1*46 


6594 


35*89 


4 


34034 


34819 




26*69 


15-02 


1*47 


66-03 


36*44 


6 






700-99 












33992 


329-18 




26*84 


1470 


1-48 


6610 


3696 


& 






96 












33947 


31014 




2699 


14*38 


1-48 


66-16 


37*44 








•92 












10 


33901 


291*06 


•89 


2712 


1407 


1-48 


6621 


37-88 



304 Mr. Marthj Ephemeria for xxxvu. 6, 

Chreenwioh Angle of Areographical Amonnt and Position Areooentiio 

Noon. Position of Western Long. | Latitade Diameter, of Greatest Defect Angle bet' 

1877. ^ '■ Axis. of tbfi Centre of i 's Disk. of niomination. Barth and 

Diff. 

o 000 //viv o e 

Not. 12 33853 271-95 -2725 1377 148 66-25 3829 

-86 
14 338*04 252*81 ' 2737 13*48 1*48 66-28 38*68 

82 
16 33754 233-63 2749 13-20 1*47 66-31 39^03 

•79 
18 337*02 214-42 2759 12*92 1-47 66-33 3935 

•76 
20 336*49 I95'i8 2768 12*66 1*46 66«35 39*6s 

74 
22 335*95 I75'92 27*76 12*40 1*45 6636 3993 

24 335*40 156-63 27*84 12-14 1*43 ^37 4018 

-69 
26 334*85 13732 27*89 11*90 1-42 66*38 40-41 

67 
28 334*29 117*99 27-94 11*66 1-40 66*39 40*61 

•64 
30 333*73 9863 27-98 11*43 1*39 66*40 40*79 

•62 

Doc. 2 333*i6 79*25 —28*00 11*21 1*37 66-41 40*96 

700*61 
4 332*59 59*86 28-01 10*99 1*35 66-42 41*10 

•59 
6 332-02 40*45 28*00 10-78 i*34 66-43 41*22 

•57 
8 331*45 21*02 27-98 10-58 1-32 66*45 41*33 

55 
10 330-88 1-57 27-95 10-38 1*30 66*47 41*41 

*54 
12 330-32 342-11 27*91 io-i8 1*28 66-49 41*48 

700*54 

14 32975 322-65 —27*85 1000 1*26 66*52 41*54 

1877 April 24 Autumnal Equinox of Mars* northern hemisphere. 

1877 Sept. 18 Winter Solstice „ „ . ,^ 

1878 Feb. 22 Spring Equinox 



M >> If 



The following list gives the areoeraphic longitnde and latitade of Ai 
centre of the disk of MarSj and also its apparent diameter, for the times d 
a number of sketches made during the oppositions of 1862 and 1864.- Nol 
to make it too lengthy, it is confined to the sketches of — 

Dawes (8 sketches in vol. 25 of the Monthly Notices, p. 225). 

Von Franzenau (6 in vol. 5 1 of the SUzwnxjsherichte of the Vienna Academy, p. 509)^ 

Harkness (2 in the Washington Observations of 1862, p. 152). 

Kaiser (2 plates with respectively 9 and 12 sketches in vol. 3 of the Annaien dm 
Sternwarte in Leiden). 

Lassell (2 plates with 24 sketches in vol. 32 of the Memoirs of the Royal Astronomic^ 
Society). 

Lockyer (4 plates with 16 sketches in the same volume). 

Rosse (6 sketches made at Lord Rosse*s Observatory, published in the same volume). 

Secchi (8 sketches made by Secchi or Cappelletti, and published in Tav. V. p. 76 a 
Memorie del Osservatorio d. Coll. Rom. Nttova Serie. Roma, 1863). 

The sketches arc arranged in the order of the longitudes of theii 
central meridians. 



April 1877. Phydcal Observations of Mars, 1877. 



305 



Anognfbieal 

l4N«. •DdLftt. of the 

CcQtno< the Disk. 

e 


Diameter. 




I-I 


-21 '2 


22*8 


Jjiissell 3 


57 


-25j2 


19-8 


M 16 


6-5 


— 2-2 


170 


Franzenau 2 


12' I 


— 22'I 


230 


Harkness 2 


12*1 


— 21*3 


22*9 


Lockyep I. 2 


i8-8 


— 21*0 


22*7 


Lassell 2 


197 


-250 


20'2 


Secchi 4 


238 


- 2-4 


17*0 


Kaiser II. 2 


24*0 


- 30 


17*2 


Dawes 10 


24*3 


- 1-9 


1 6*8 


Franzenau I. 


267 


-21*3 


22*9 


Lockyer I. 3 


28*2 


— 2-1 


16-9 


Kaiser U. i 


29*0 


-25- 1 


20*0 


Seochi 5 


395 


-25-3 


195 


Bosse 5 


45-0 


-265 


13*4 


Kaiser I. 7 


48*2 


— 25'0 


20*2 


Lassell 15 


491 


- 26 


17-1 


Dawes 12 


494 


—207 


22*5 


Lockyer I. 4 


498 


- 9 7 


157 


Kaiser II. 7 


'59 


— 207 


22*5 


Loekyer II. i 


605 


- 23 


17-0 


Dawes 13 


692 


-24-8 


20'5 


Lassell 14 


75-1 


— lo-i 


11*2 


Dawes 15 


770 


— 24-6 


20'9 


lASsell 13 


808 


— 20*5 


22*1 


„ I 


838 


- 9 3 


160 


Kaiser IL 8 


85-3 


— 24*2 


214 


Seochi 3 


862 


— 20-6 


22*4 


Bosse 3 


• 864 


-249 


20'4 


Kaiser I. 3 


943 


-24-2 


214 


Lockyer U. 2 


»3 5 


-205 


22*2 


Bosse 2 


1 188 


-26s 


14-8 


Kaiser I. 6 


1198 


-265 


15-0 


liassell 22 


1232 


- 8-4 


i6-6 


Kaiser II. 6 


1275 


- 1-2 


1 6*4 


Dawes 2 


1283 


— 24*2 


21*4 


Lassell 12 



llmeB aasigaed to the Sketches. 



Gr. 



tt 



1862 Sept. 22*44 
Oct. 27-31 
64 Nov. 10 9*' 30" Vienna. 
62 Sept. 30 ii"* Washgt. 

23 ii*" 55" Gr. 
20*44 n 

Oct. 25 8" Borne. 

64 Nov. II lo*" 30" Leiden. 
14 12* o" Gr. 
8 9* 30™ Vienna. 
62 Sept, 23 i2'» 55™ Gr. 
64 Nov. 9 9'> 35" Leiden. 
62 Oct. 26 9'» 15" 
29 I*" 
Dec. 2 8" 35" 
Oct. 2538 
64 Nov. 12 12*" 30" 
62 Sept. 17 lo*" 50* 
64 Dec. 18 10^ o" 
62 Sept. 17 ? 

64 Nov. 10 12* 6" 
62 Oct. 23*39 

65 Jan. 21 8^ 
62 Oct. 25-36 

Sept. 13439 
64 Dec. 15 lo*" 30* Leiden. 
62 Oct. 18 8" 13" Borne. 

Sept. 16 23'' 55" Sid. T. Birr C. 

Oct. 24 II* 25" Leiden. 

Oct. 18 8* Gr. 

Sept. 14 o* 26 Sid. T. Birr C. 

(assuming the time to be o** 26" 
instead of 6* 26") 

Nov. 23 7'> 50" Leiden. 

22-29 ^^* 

64 Dec. 10 10* 10™ Loiden. 

Nov. 3 12'' 24" (ir. 
62 Oct. 1 8*43 „ 



tm 



Borne. 

Sid. T. Birr (X 

Leiden. 

Gr. 

II 
}» 
Leiden. 

Gr. 

II 
II 
II 
II 



3o6 



Mr. Marth, Ephemerisfor 



IXIYD. 5, 



Areographlcal 

Long, and Lai. of the 

Centre of the Disk, 
o o 


Diameter. 




Times aflrigned to the Skrtahw. 


137-2 


-24-1 


21*5 


Lassell 11 


1743 


Gr. 


137-5 


-23-9 


21-8 


Lockyer II. 3 


15 9* 8- • 


It 


? 1405 


It 


It 


II n.4 


put 9** 20" 


t> 


144.4 


-23-9 


II 


Lassell 10 


15*40 


ft 


1537 


— 26-4 


15*7 


II 21 


Nov. 18*28 


tf 


162*1 


-23-7 


22*0 


9 


Oct 13*40 


It 


162-3 


— 26-5 


iS'S 


Kaiser I. 5 


Nov. 19 8* 15" 


Leiden. 


163-0 


-26-4 


158 


Lassell 20 


17*28 


Gr. 


1 68- 1 


— 26-4 


16-1 


S6cchi8 


16 7* i6"^ 


Borne. 


1797 


-23-4 


22-3 


Lassell 8 


Oct 11*40 


Gr. 


1 88-6 


-26-3 


16-3 


1. 19 


Nov. 15-30 


It 


1958 


-23-4 


22*3 


Kaiser I. 2 


Oct. II ii»» 0^ 


Leiden. - 


1999 


-IO-8 


12*9 


,1 n. 12 


65 Jan. 7 S" 0" 


ti 


201 '2 


-234 


223 


Lockyer III. I 


62 Oct II II* 4" 


Gr. 


2147 


-23-1 


22-5 


n m. 2 


9 io*» 47" 


ti 


2201 


- 6-2 


17*3 


Kaiser 11. 5 


64 Nov. 29 10* 10^ 


Leiden. 


221*4 


— 26-2 


17-1 


Secchi 7 


62 Nov. II 7* 45" 


Borne. 


2337 


- 6-6 


173 


Dawes 4 


64 Dec. I 12* o» 


Gr. 


2364 


-108 


135 


Kaiser IL 1 1 


65 Jan. 3 8* o» 


Leiden. 


2381 


— 26- 1 


17*4 


iSecchi 6 


62 Nov. 9 7>» 38" 


Borne. 


2402 


— 202 


21-3 


HarkneBS i 


Sept 6 I2»» 


Waahgt 


2487 


- 4-2 


17-4 


Franzenau 4 


64 Nov. 20 7'* 30" 


Vienna. 


2530 


- 4-6 


175 


» 6 


22 9'* 0" 


II 


2633 


— 22-4 


229 


Lockyer IIL 3 


62 Oct. 3 lo** 30" 


Gr. 


264- 1 


— 260 


11*7 


Kaisor I. 9 


Dec. 14 6^ 45" 


Leiden. 


271-8 


— 227 


229 


L I 


Oct. 5 12'' 35» 


It 


2743 


- 5-6 


174 


Dawes 6 


64 Nov. 26 1 1** 46" 


Gr. 


276-2 


— 22*4 


22-9 


Lockyer III. 4 


62 Oct. 311'* 23" 




278-0 


-232 


146 


Rosse I 


July 22 22'* 30" 


Sid. T. Birr I 


280-4 


- 4-2 


174 


Franzenau 5 


64 Nov. 20 9'* 40" 


Vienna. 


283-0 


— 224 


229 


Lockyer IV. i 


62 Oct 3 ii** 51" 


Gr. 


2833 


-228 


227 


Rosso 4 


6 2^ lo" 


Sid. T. Birr 


2876 


-259 


181 


Lassell 18 


Nov. 5-32 


Gr. 


2902 


- 47 


17-5 


Kaiser II. 4 


64 Nov. 22 lo** 45" 


Leiden. 


2908 


— 106 


14*3 


„ XL 10 


Dec. 28 8" o" 


•1 


2959 


— 21-9 


230 


Lassell 7 


62 Sept. 29-43 


Gr. 


2967 


-25-8 


183 


,1 17 


Nov. 4-32 


ti 



il 1877. Phyneai Observations of Mars, 1877. 



307 



|x«|»liieal 
lLiU.afthe 

rtheTMiik. 




Diameter. 


• 


Times assigned to the Sketches. 


— 26-1 


12*1 


Lassell 24 


Dec. 11-29 Gr. 


— 2I«6 


• 230 


Secchi 2 


Sept. 26 9*» 45" Rome. 


-217 


230 


Lassell 6 


2745 Gr. 


- 3*2 


I-7-3 


Fraozenan 3 


64 Nov. 15 9'» 30" Vienna. 


—26-2 


12-3 


Kaiser I. 8 


62 Dec. 10 8^ 15" Leiden. 


i - 4-2 


17*4 


Dawes 8 


64 Nov. 20 1 1"* 36" Gr. 


: - 4-0 


174 


Kaiser II. 3 


19 ii*" 20" Leiden. 


; -26-3 


I2'5 


Lassell 23 


62 Dec. 829 Gr. 


> -259 


17-9 


Rosse 6 


Nov. 6 i^ 40« Sid. T. Birr C. 


^ — 21*1 


22*8 


Secchi I 


Sept. 21 20^ 50" Sid. T. Rome. 


; — 2i*s 


22'9 


Lassell 5 


25-44 Or. 


tt 


M 


Lockyer IV. 2 


lo*" 44" Finished. 


* fi 


f» 


,. IV. 3 


10^ 50- 


i -21-3 


22*9 


,, IV. 4 


23 9" 40" 


^ -21-4 


22-9 


Iiafisell 4 


24*44 


^ -25s 


19*1 


Kaiser I. 4 


Oct. 31 8'» 45" Leiden. 


I -21*3 


22*9 


Lockyer I. i 


Sept. 23 lo"* 25'" (Jr. 


S — IO-2 


iS'O 


Kaiser II. 9 


1864 I>ec. 23 9* 25" Leiden. 



ic(M>ant of the uncertainiy of the times assigned to the sketches, 
^tades of the central meridian may, of course, be considerably tin- 
an uncertainty of 1° of areograpbical longitude corresponding to 
"•1 in time. 

interpolating the longitudes given in the Ephemeris for the times, 
•bservations are to be taken, and consulting the corresponding 
s, trustworthy observers may properly prepare themselves for 
bheir attention upon the most desirable observations which can 
t made. Amongst the most important are careful observations of 
les and places of the passages across the central meridian of all 
3t distinct and well defined points on the planet's surface, which 
trve as fundamental points of Areography. Foremost amongst 
pe the point / (the neck of the hoar-glass), the spot a (the end 
serpentine), and the centre of spot d (the pupil of the eye) of 
*8 map of 1830. Since, in observing, the diameter of the disk 
h passes through the southern polar spot S — will have to be 
as the central meridian, the observations will require to be 
ed, not only for phase, for which the Ephemeris supplies the 
iry data, but also for the non-coincidence of S with the southern 
3r the determination of which series of carefully observed angles of 
n of S are required. It is to be hoped that astronomers who 
:he requisite instruments at their service will not let slip the 
imities of the approaching opposition for making substantial 
Imtions towards our better knowledge of Mars. 



3o8 Lord Lindsa/y <md Mr. GiU^ BeauUs of xxxviL 6, 



Note on the Results of Heliometer Observations of the 
Planet JuuOf to determine its Diurnal Par Max, 

By Lord Lrindsaj and Mr. David Gill. 

The reduction of the observations inade with the heliometer 
for determination of the diurnal parallax of Juno at ManritiiiB 
being finished, it may be of interest to present the final resnlts 
to the Society in anticipation of the full details now in tihe piess, 
forming vol. ii. of the Dun Echt publications. 

Corrections of the tables of the planet were obtained, fonnded 
on the results of meridian observations at Greenwich and Waah- 
ington, and a fine series of extrameridian observations mjade by 
Mr. Willson at Cambridge, U.S. In this latter series the stars 
of comparison were determined by Mr. Rogers with the transit 
circle of the same observatory. 

Two systems of corrections were so obtained, founded on 
somewhat different expressions, greater weight being given to 
the Cambridge observations in the second system. 

The computations were made separately on both systems, 
with the following result : — 

xst system. and tysteiu. 

Moan O parallax 8"77+o"-04i 8"76+o""aj2 

From the late arrival of the yacht at Mauritius, the observa- 
tions could not be commenced until a week after opposition. 

In consequence of this barely one-third of the anticipated 
number of observations could be secured, and these, in conse- 
quence, with small parallax factors, rendered still smaller by the 
fact that stars of comparison could not be obtained in the most 
favourable positions. 

This being, so we do not present the result as a determination 
of the parallax possessing a high weight. There is a discordant 
value on November 15, which in a larger series would have pro- 
bably counter-balanced by another, in which all the sources of 
error had combined in the opposite way; and thus, if we are 
asked what we believe to be the most probable value resulting 
from the determination, we should reject this result. The values 
then become 

ist system. and system. 

8"-82 8' -81 

and these we believe to be exceedingly close approximations 
to the true O parallax. 

At the same time we are aware that the rejection of any 
observation is quite unsound ; and we simply present these 
values, not as a determination of the parallax, but as the result 
of a first experiment, made under somewhat trying and difficult 
circumstances, from which conclusions can be drawn as to the 
future value of the method. 

That which wo desire now more particularly to bring before 
the Society is the following table, showing the residuals in the 



April 1877. Observations 0/ Juno etc, 309 

eqaations when the errors of the star places have been eliminated, 
and ihe first-mentioned values of x are substituted in them. 

Each equation from which a residual results is the arith- 
metical mean of all the equations resulting from the comparisons 
in each epoch, so that the residuals show actually the errors of 
the obeeiTations in distance of each evening and morning. 

A reference to the map of the path of Juno, published in con- 
nection with our paper in vol. xxziv. p. 279 of the Monthly 
NoUeea of the Society, will show the stars of comparison 
referred to. 





1 


Star of 
Ooupflzison. 


xst 8}'Btem. 


and Rjntom. 


Kov. 13 


Erening 


e 


+ 0088 


+ 0103 




Morning 


e 


+ 0129 


+ 0134 


13 


fivening 


$ 


— 0038 


-0034 




Morning 





-0084 


-0094 


15 


Evening 


C 


— 0074 • 


-0075 




*t 


A 


+ 0*1 14 


+ 0-113 




Morning 


C 


+ 0206 


+ 0199 




ft 


A 


-0-213 


— 0-206 


18 


Morning 





-0003 


— o-ooi 




ft 


M 


+ 0*012 


+0-023 


19 


Evening 


$ 


+ 0*021 


+ 0-024 




a 


M 


— 0016 


-0020 


^3 


Evening 


1 


+ 075 


+0053 




») 


X 


-0080 


—0060 


24 


Morning 


I 


— 0*I02 


—0*069 




»> 


X 


+ o*ioi 


+ 0073 


25 


Evening 


M 


— o*o8i 


-0134 




Morning 


M 


— 0*004 


—0*042 


26 


Evening 


M 


-0153 


-0176 




Morning 


A* 


-0051 


-0073 


29 


Morning 


tf 


— 0019 


— o-i8o 


^0 


Evening 


V 


-0194 


-0*259 



The resulting probable error of a complete comparison de- 
duced from this table is di o''*o75, coofirming beyond all doubt 
the conclusion at which we arrived in the paper referred to, viz : 

Tliat hy means of the Helioiiieier it u possible to determine 
the distance of a minor planet from a single star near it, or to 
interpolate lis place relative to two distant stars, ivith a 
probable ei'ror less than ,\y th of a second of arc, 

A ?^ear star is one whose distance is less than 1000'' from the 
planet. 

A distant star, from 1000" to 7000". 



3 10 Mr. Oill^ On jftroposed Expeditiwi xxxvn. 6, 

On the proposed Expedition to observe the approaching Opposition 

of Mars. By Mr. David Gill. 

The approacliiiig opposition of Mars is the most favourable 
of the century for determining the Solar Parallax, the horizontal 
parallax at opposition being within 5 per cent, of the difference 
of the horizontal parallax of the Sun and Venus at the Transit 
of 1874. 

Daring six weeks observations can be made in conditions of 
temperature and of freedom from hurry or excitement infinitely 
more &vourable to good observations than those afforded by the 
Transit of Venus, By observing the diurnal parallax, the ' same 
observer gets a result which is entirely free from errors of 
personality, and he also obtains a factor of parallax larger than 
can be obtained by any two existing observatories. 

So early as 1857 the Astronomer Royal called attention 
to the present opposition, and then expressed his opinion — an 
opinion to which he still adheres — that observations of the diurnal 
parallax of the planet at such an opposition present the best 
means of determining the Solar Parallax. 

The method proposed by the Astronomer Royal was to ob- 
serve the difference of R.A. of the planet and stars in the evening 
and morning, and by such a method, with a proper equatoreal and 
a skilful observer, there is no doubt that results of very high 
accuracy could be attained. The success which has attended the 
observations of Jimo (the results of which are communicated to 
the Society to-night) led me to believe that the original plan of 
the Astronomer Royal might be somewhat modified, and the 
heliometer successfully substituted for the ordinary equatoreal, 
according to a plan of observation afterwards described. 

I applied in the first place to Lord Lindsay, who, in the 
kindest manner and with the most complete sympathy with the 
purposes in view, at once placed the instrument at my disposal. 

I then submitted detailed plans of the proposed observations 
to the Astronomer Royal, to the Council of this Society, to Prof. 
Adams, and to Dr. Robinson and Mr. Hind, and I gratefully 
acknowledge the support in the matter which I have received 
at their hands, as also the promises of substantial assistance, 
should it be required, which T have received from Sir George 
Airy, Mr. De La Rue, Mr. Proctor, and others. I have also con- 
sulted Dr. Auwers of Berlin as to several details of these plans, 
and have now, as at all times, received from him the kindest 
and most valuable assistance. I now beg to present to the Society 
the following plan of the proposed observations : — 

Selection of Place of Observation. 

In heliometer observations distances are mcasurcd with 
much greater accuracy than position-angles, therefore'we should 
endeavour to select stars nearly vertically above or below the 



April 1877. to observe Opposition of Mars, 311 

planet if we wish to iiave the full amoTmt of parallactic displace- 
ment most advantageously measured. The star which is verti- 
callj above or below the planet in the evening observations 
(neglecting the planet's motion) can only be vertically above or 
below the planet in the morning in one case, and that is when the 
observer's station is on the equator and the star's and planet's 
declination are both 0°. 

When the planet has any other declination, we must endea- 
vour to select a station in which the planet is on the prime 
T^ertical at the mean altitude of observation (found practically 
to be 30°), and to select the stars of comparison of the same de- 
clination with the planet. The observations evening and morning 
are then symmetrically disposed as to parallactic displacement. 
In the case of Mars at the present opposition this condition 
is realised in a latitude about S° S. 

The meteorological conditions are also, of course, all-im- 
portant, and it has been suggested to me that I should occupy 
some raonless district in the highlands of Pern, affording almost 
the certainty of clear weather every night. There appears to 
be a very serious drawback, however, in the great difference of 
temperature between day and ni^ht. It is no unconmion thing, 
in the higher districts there, to nave a temperature verging on 
1 00® Fahr. by day and freezing by night, and I feared, however 
perfectly and symmetrically the comparison stars and observa- 
tions may be arranged for the elimination of progpressive change 
of scale- value, that errors due to temperature may yet creep in 
which might have a systematic character. 

In this respect insular stations have a great advantage, and 
after much consideration I have selected the Island of Ascension — 
originally suggested to me by Lieut. Neate, R.N. — as the most 
saitable site. Its geographical position is almost absolutely the 
best possible, and to Mr. Scott and Captain Toynbee I am in- 
debted for a copy of a work, just issued by the Meteorological 
Office, on the meteorology of this island. 

The proportion of cloud is from 5*0 to 6'o (10 being total 
obscuration) for the date and hours of observation, a propor- 
tion smaller than Mauritius, where the conditions were suf- 
ficiently favourable^ Two or three degrees appear to be the 
"kranoige of temperature between 6 p.m. and 6 a.m. 

Selection of Stars of Comparison, 

In making this selection, a complete list was independently 
"pTepared of all the stars of 8th magnitude or brighter near the 
>atn of Mars contained in the following catalogues : — 

Catalogue of the Berlin Academy Star Maps. 

Weisse's Bessel. 

Lalande. 

Santini. 



312 Mr. QtUy On proposed Expedition xxxm. 6, 

These were all independently reduced to 1877*0 and plotted on 
a chart, together with the path of the planet. It proved that 
seyeral very important stars were omitted in Bessel's Catalogue ; 
the reason, I believe, being, that when that Astronomer fonnd two 
stars in the field and could not observe both, he always chose the 
fainter star, leaving the larger star to other observers, as less 
likely to be overlooked by them. 

Such an omission is the star marked g (y^ mag.) in the cata-. 
logue, which is very important, because on September 5 the planet 
approaches within 2' of this star. 

In the selection of the stars of comparison, I have been 
guided by the following considerations : — 

1. It is desirable, if possible, and if consistent wiiii the main 
end in view — the parallax determination — ^to make the 
most accurate determination possible of the abaolate 
place of the planet for the purposes of gravitational 
astronomy. 

2. Position-angle measures being greatly inferior to measims 
of distance in point of accuracy, the determination of 
absolute positions will be best secured by relying on the 
distance measures only. 

3. The minimum number of stars by which an absolute 
place can be secured by distance measures is three, and it 
is not desirable to measure more, because to measure firom 
three stars syknmetrically will require nearly all the time 
which the measures should occupy. 

4. The planet must be contained within the triangle formed 
by the three stars of comparison ; and, since the change 
in B.A. is the most important, two of the stars should to 
about the same declination with the planet, and as nearly 
as possible equally distant from it. When this is noib 
possible, the stars must be arranged to determine rigidly 
the displacement in B. A., sacrificing, if necessary, the dech- 
nation. 

5. When stars can be found sufficiently bright, and nearly of 
the same declination with the planet, not more than 2000'' 
or 3000" apart, then the method of two stars, employing 
position-angles, is best if the planet is nearly in the line 
joining the stars of comparison. 

In the equations of condition which result &om measures of 
distance with stars so selected, it is always possible to consider 
the error of the scale- value an unknown quantity, and to deter, 
mine it from the stars of comparison in each group of observa- 
tions. This is the best method for complete elimination of Byste-> 
matic error when the places of the stars of comparison are 
determined with tolerable precision. 

To secure such precision, as well for this purpose as for the 
determination of the absolute place of the planet, the places of 
the stars of comparison must be determined by meridian observa- 
tions; and to increase the precision of the result, the whole of 



April 1 87 7. to ohserve OppodUon of Mars, 313 

the stars should be \K)nnected by a heliometric triangnlation. 
To effect this it has been necessaiy to introdnce a few additional 
stars, in general denoted by Ghreek letters. 

I have also included in the list the star \p^ Aqiiarii, because 

peculiar interest attaches to it from the fact that it was occulted 

by Mars in 1672, October i. The occultation was observed by 

fiicher at Cayenne, by Picard near Beaufo'rd, and by Boemer 

at Paris, and the observations are in very close accordance (Le 

Verrier, Oomptes BenduSf 1872, July 22). In this paper, M. Le 

Verrier deduces the Earth's mass, and thence the solar parallax, 

from the secular variation of the plaiiet's longitude produced in 

't^wo centuries by the action of the Earth, employing the occulta- 

t:ion just cited with Bradly's observations of the star, on the one 

liand, and modem meridian determinations on the other. 

The present opportunity for making a rigid determination of the 

jp1anet*B heliocentric place is infinitely more favourable than that 

of 1672, because the determination can be made to depend upon 

so many stars. There is no doubt that, if many observations of 

-the stars of comparison and of fundamental stars are made at 

different observatories and with different meridian circles, and 

the heliometer observations have even moderate success, a 

determination of the heliocentric place of the planet will be 

secured of flEur higher accuracy than any hitherto obtained. 

I therefore most earnestly solicit the co-operation of obser- 
vatories possessing good meridian instruments in this work, 
and shall gratefully acknowledge said utilise any such observa- 
tions communicated to me, aiddressed to the Booms of the 
Society. 

Mr. Hartnup, at Liverpool, has most kindly volunteered to 
apply the splendidly rigid Equatoreal of his Observatory to the 
determination of the differences of R.A. and declination of these 
stars of comparison . These observations will chiefly strengthen the 
heliometric triangnlation, but do not supersede the desirability, or 
even necessity, for good meridian observations also. 



3M 



Mr. Gill, On proposed Expedition 



xxxyn. 6, 









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Plan <if Heliometrie Triang^aUcm of Stan to be eompar$d wUk 1 


8Un. 


Mag. 


R.A. 
h m 8 


/ 


Portion Angle. 




a — 6 


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12 33 


344*9 


a— a 


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2468 


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e— « 


8-8 


3 15 1 


[2 32 


2768 


»-*>Aq. 


9-^5 


7 15 1 


[O 28 


2174 


«-/ 


9-6-7 


6 40 ] 


[I 16 


2831 


«-y 


9-7-8 


6 59 ] 


[I 42 


3184 


»— * 


9-6-7 


8 9 1 


[I 47 


3087 


»— € 


9-8 


.5 18 1 


II 53 


355-3 


— / 


8—6-7 


6 54 1 


ti 59 


208-1 


•-^ 


8—7-8 


7 14 1 


[2 25 


246*1 


•— * 


8-7 


8 24 1 


12 30 


261-2 


t— * 


8-7-8 


9 5 


12 44 


278-2 


/-♦•Aq. 


6-7-4-5 


852 1 


10 33 


1903 


f-S 


6-7-7-8 


8 36 


II 48 


349*7 


/-* 


6-7-7 


946 


II 52 


3247 


/-♦• 


6-7—5-6 


10 25 ] 


10 49 


224*8 


/-* 


6-7—8 


11 23 ] 


[I 17 


264-4 


/-* 


6-7-7-8 


10 27 


[2 6 


324.7 


9-^ 


7-8-8 


4 57 1 


[2 21 


83-2 


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7-8-7 


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[2 19 


284-8 


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10 46 ] 


12 33 


304-4 


#-« 


7-8-8 


II 42 ] 


II 43 


232-9 


JLA^-C 


#-$-» 


13 II 


9 55 


2798 



April 1877. 



io chserve Oppoaition of Mars. 



317 



lUg. 

4-5-5-6 

4-5-8 
6-7—8 

6-7—7-8 

5-6-8 

5-6-8 

7-8-8 

8-8 

8-9 
8—6-7 

8-6-7 

8—9 

9-7 
9—6-7 

9-6-7 

6-7—7 
6-7-7 
6-7—8 

6-7-7-8 
7-8 
8—7-8 

7-8-7 
8—6-7 
8—5-6 
8-7-8 
8-8 

8—6-7 

8-9 

8-9 

8-9 
8-8 

8-6-7 

8-8 

8-7-8 

8-8 

8-8 



R.A. 
h m 8 

23 II I 

11 58 

12 52 

11 $6 

14 45 
13 32 
13 33 

15 42 

17 22 

18 5 

19 47 

18 35 
23 9 

20 57 

21 27 

23 52 

24 22 

25 56 

26 10 

27 35 

29 23 

30 46 

13 56 

14 35 

14 37 

15 33 

19 8 

18 25 
23 16 46 
22 54 49 
57 3 
55 34 
59 16 

5845 

22 59 30 

23 I 47 



Deo. 



I 

o 29 

1 48 

2 37 

II 

045 

2 2 

o 38 
o 58 

1 40 

I 

24 

1 12 
I 25 
O 20 

1 54 
o 49 

36 

9 42 

1 28 

21 

9 23 

1 55 

52 

2 9 

1 20 

I 47 

1 5 

46 

2 19 

2 23 

3 17 
3 7 

1 58 

2 39 
2 43 



Position Angle. 

o 

3047 
319-5 . 

213*8 

3245 
258-6 

3328 

195-5 
2078 

2511 

297*5 
2653 

3085 

304-4 

345*9' 
217-8 

2481 

334-2 

309*0 

253-9 
2388 
184-5 
256*2 

54*4 
1396 

34-9 
115-5 

298*2 

2305 

183-3 
123-9 

1525 

528 

312-2 

191*6 

2430 

262*8 



Distance. 

56 
114 

85 

34 
66 

62 

103 

77 
90 

119 

85 

63 
104 

87 

58 

70 
116 
122 
108 

52 
107 

33 
96 

92 

102 

35 
85 
69 

83 

"3 

62 

89 

49 

106 

48 
III 



B B 2 



3i8 



Mr. QUly On proposed Eapediiion 



ZXIYIL 6, 



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Afril 1S77. to oh§erv6 OfpoaUion of Mart. 319 



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Mr. only On proposed Expedition XXXYU. 6, 



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April 1877. to oh$erve Opposition of Mars, 321 












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322 



Mr, OtUf On proposed Expedition 



XXXTIL 6, 



/ 



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April 1877. to dbterve 0£po9Uion of Mars. 323 



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Mr, OiUf Oh proposed Expeditioii 



xxxvii. 6, 



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326 



Mr, Qil\ On proposed Eaipedition etc. 






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April 1877. Mr, CKH^ On the Opposition etc. 327 



On the OpposiHon of the Minor Planet Ariadne as a mea/ns of 
determinvng the Solar Parallax. By Mr. David Gill. 

The minor planet Ariadne (43) is in opposition on Jnly 24 
d the present year, in circnmstances very favourable for deter- 
mining its dinmal parallax by the heliometrio method. The 
distance of the planet from the Earth is o'83, the Snn's mean 
distance from the Earth being i. 

Its declination ( — 15°) is not far from the most favourable 
position for observation at Ascension, and opposition occurs ten 
before it is possible to begin to observe Mars satisfactorily, 
le observations can therefore be made without inconvenience 
additional expense. 

It is true the planet is somewhat faint (8*8 mag.), but 
perience at Mauritius has taught me that with such a 
rliometer as Lord Lindsay's, in a tropical sky, 8*5 mag. stars 
»ii be measured with more accuracy than any other, and that 
mag. stars can be well measured in £ftvourable atmospheric 
c^onditions. 

The geometrical conditions are very much more favourable 
^-n^n in the case of Jwno (the distance of Jrmo at opposition was 
-^ ^05) ; and, besides, it is possible to select more suitable stars of 
^^Omparison. The opportunity therefore appears a very good 
^*^e, and I have accordingly selected stars of comparison, of 
^^hich the: subjoined is a list. 

Xn addition to this list, absolutely req aired for comparison 
^^th the planet, are a few stars required in the triangulation of 
'**h© comparison stars, the latter are denoted by Greek letters. 

The plan of observation is given in connection with the 
^oIXq^^^^^i^ tables, as also the plan of triangulation of the stars 
^^ oomparison. 

I shal) be 'greatly indebted to any astronomier who will assist 
determination in any of the following ways : — 

1. By meridian observations of the stors of comparison. 

2. By extra-meridiaji determinations of the difference of B.A. 
i declination of any of the stcu:^ of comparison, but especially 

^y accurate measures of the difference of declination of the stars 

«/> c. These stars will be used by me to determine the zero 

^^ the position-circle in the triangulation, and, as they do not 

^^ffer 2' in declination, the observation can be made by means 

^f the wire micrometer with very great accuracy. 

3. By heliometer measures, either of the star and planet, 
^^ of the distances and position-angles of the stars included in 
^^^ plan of triangulation. 

4. By a series either of meridian or extra-meridian observa- 
tions of the planet, extending as far as possible on both sides of 
opposition. 

The oppositions of Iris (7) and Melpomene (18) are also very 
^Yonrable. I will notice them more at length at the next 
nteetin^^ of the Society. 



328 



Ur. am, On the Opporition 



xzx?n. 6, 



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April i877* 



as a meam etc. 



329 



Ifm qf Bdhautr i o TVitmgwiatiom qf Stars to be compared with Ariadne. 



7-8—8-9 

7-8-7-8 
8-7-8 



8—7-0 



-y 



7-8—7-8 
7-8-9 



-y 



7-8-7-8 
7-«-9 
7..8— 8^ 

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7—7-8 

7—9 
7-8-9 

8-9-9 
8-9-8-9 
7-8-9 
7-8—8-9 

9-8-9 
9-7 
9-8-9 
9-9 



BJL 
h m • 
20 10 19 

12 33 

14 22 

15 17 
15 48 
1446 

15 41 

16 12 

17 29 

17 52 

18 I 

19 21 

1847 
1856 

20 16 

21 43 

19 19 

20 39 

22 6 
28 22 

23 24 

24 45 

26 12 

25 46 

27 13 
20 48 

22 15 

23 35 
27 37 
2838 

25 o 

20 26 27 



Decs. 

o 



Poiiti<m Angle. Diet. 

r e I 

54 241-6 61 

16 283-0 67 

I 345*2 46 

39 270 64 

56 2906 97 

28 257-8 108 

I 230*0 68 

18 262-8 80 

50 234-6 1 16 

56 322-0 43 

I 318-8 57 

28 241*2 48 

3 3007 94 

18 309-0 14 

45 «95o 59 

20 2845 56 

42 2372 114 

49 1837 66 

25 276-6 43 

47 2302 1 1 1 

57 3428 99 

13 86-5 115 

48 44*2 109 
10 86*6 34 
36 99*2 106 

58 I45'9 "2 
52 331-2 81 

14 226*5 81 
48 209*0 87 

31 1700 44 

18 3370 57 

10 67*8 90 

32 134*9 58 



330 



Mr, OUlj On the OpposUwn 



XXXYII. 6y 



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April 187 7* of Ariadne M a Meani etc, 331 









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CJ w ^ 10 QO *^ 



**«o»^^t^** ^eo*o«p M o ovo •* "* P o fovo ^o ^>o 






I 









CO 0^ O '- N 

M M c) M M 



C C 



Mr, Oittf On the Opponium 



XXIYIL 6f 









00 -O^ H 
•* « « 



M M f« 



M el M 



f^ 00 CO t> 00 O t<» 



J^»oqo«o« Ot^<^^ O"^.© 



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to 



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Za eMMMMM»i«M*i4MMMMMMMMMMMMM 



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^ 43 « 



\0 l»*^^«*>^0>0 M eO^O »r» 



M 0\ M ro O 
u-> m ro N to 



M fl to O M «n 




»*0 O o M t>i«^^*•r*.Qto^*>to«*>^0^^»^^^ Q 



•£?0 »*^»^M t<*** « « ^*»^o 6 «oo tn« o\tntni^ 
Mm O^nO rsiOvN^O moq oofS cioociQO toi^QO »or«. 



to « N 



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Q \O»^MQ0^0 mO\0 t^N O MOO •5.?10\ 



,A< jjOO QO C^^nO t^^^fO^^^O M fO>0 »Om fOVO O « to 

^^ Urn ^ ^ ^ ^ ^ ^ ^ ^ m ^ ^ ^ ^ ^ ^ m ^ ^ ^ ^ 



I ii-*i5'i-*^:i:m^i5i*x 




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1 1877. 



cf Ariadne at a Meant eie. 



333 



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334 



M, Sieplum^ Ohservaiions of 



IXXYIT. 6f 



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Apfil 1877. 



New Nebulue cU Marseilles. 



33S 




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NO 



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31. Stephany Oh^ervatums qf 



xam 



Pimtums Mopenne* de» StoUet ds 



pour 1876-a 



Komt d« ^ioOes. 



dioitet. 
h m ■ 



ft 



a 


88 Aig. Z> 2 


34 5859 


87 4541 


A. C»t. de Weisse, 
N» 583 H. a 


b 


92 Azg. Z-f 2 


35 40^27 


87 12 57*8 


I obs. m^ridienne. 


e 


129 Aig. Z+35 


35 4r97 


54 20 24*6 


I obt. mirid. 


d 


169 Arg. Z •»- 10 


I 15 9'6i 


79 22 41*1 


A. Cat de WeiBse, 
»• 215 H. I. 


e 


236 Arg. Z + 20 


I 26 2'34 


69 15 i6*8 


I olm. mind. 


f 


290 Aig. Z+34 


I 32 34-98 


55 18 565 


I o\m. m^rid. 


9 


311 Aig. Z+30 


I 50 58-19 


59 18 54« 


I obs. m^rid. 


h 


359 Arg. Z+3I 


I 56 2464 


58 42 32-1 


I obs. mirid. 


% 


456 Aig. Z 


2 49 4987 


90 42 80 


I obs. miiid. 


• 


451 W. (ax,); 
H. xxi. 


21 20 49*09 


97 32 580 


A. Gat de Weisse, 
N*45i H. jad. 


k 


238 W. (tf.c.) ; 
H. xzii. 


22 13 23*06 


9441 II-3 


A. Cat de Weisse. 


I 


4794 Arg. Z+35 


22 19 50*96 


54 27 30 


I obs. m^rid. 


m 


4744 Arg. Z 4-16 


22 21 3795 


73 5* 21*7 


I obs. m^d. 


n 


4531 Arg. Z + 33 


22 27 3657 


56 41 383 


A. Cat. de Weisse, 
N« 584 H. xxii. 





4561 Arg. Z + 33 


22 34 26*29 


56 32 14*0 


I obs. m^d. 


P 


4953 Arg. Z + 39 


22 46 41-51 


50 23 35 


Cat de Groombr., N« 


9 


4942 Arg. Z + 35 


22 55 3-89 


54 49 355 


I obs. m^rid. 


r 


4674 Arg. Z-»- I 


22 56 3572 


88 26 31-3 


I obs. m^d. 


s 


4858 Arg. Z + 34 


23 4 55*io 


55 50 >4-5 


I obs. mdrid. 


t 


471 1 Arg. Z + 23 


23 9 35«3 


66 15 65 


2 obs. m^rid. 


u 


4766 Arg. Z + 24 


23 18 5-34 


65 40 74 


I obs. m^rid. 


V 


4641 Arg. Z + 27 


23 48 3858 


62 27 36 3 


I obs. m^rid. 



April 1877. 



Nmo Ne/ndm al ManeiUa. 



337 



GQ 



4 



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il. Sttphan, Ohtenaiumi t^ . .zxxvil 

i 111 I! nl| I ili 1 

|1 !||lll a? 1 1 lip. I 
*| iMif Jill? IP^ I 

I a. H ? -8 1 IM • • 1 1 j'' i lis f 
— — ! 

I'S S R :•*!!, j •» tr ~ j ■2 X S," B, =, I 

|.j sssss's, s. s, s, a a^js s 8. g 

j 
If SSSiK"""*:? I 




ffJffSjrK » » 



AptO 1877. Ne» Nebula at ManeOhe. 



fotiUoiu Hef/mntt dti 6Mie* dt Comparaiaon pour i877'0. 



< «' Aig. Z+43 a 6 3478 

' 473 Aig. Z+34 a aS 50-69 

f luxatjm 3 30 8-04 

/ «9Arg.Z+ 4 343 35-74 

f 3S8 Aig. Z+ 3 1 43 47-16 

* 875 W, (*c,) ; 3 SO 58-31 



> «i0 4ig,z+a3 3 51 3-56 

• »7iA^Z+as 3 57 a979 
' JMW. («.)j 4193954 

fl.i». 
■ I'*4ig. Z+34 50 317' 

• '3SW. («jj,); S 733-53 100*6539 C»t.W. 

H.T. 

• 'JS« W. (tfjr.); 6 I 877 99 43 33 3 Cat. W. 



DMutin 


Aatorit*. 


93 37 32-9 


CaL Weisse. 


4fi I i-S 


I obNimUoD miaiit 


45 59 39S 


I obg. mJrid. 


55 3 '57 


1 oba. mirid. 


101 30 7-3 


1 oU. mirid. 


85 53 '54 


I obE. mirid. 


85 57 i6-3 


1 ob>. mMd. 


100 5» 14-4 


1 obfl. mirid. 


95 58 389 


Cat. WoImb. 


«7 14 555 


I obi. mind. 


64 53 59-4 


I oha. mirid. 


95 36 4-.I 


Cat^W. 



' >i9« Ajg. Z+44 


7 3 31-66 


45 "9 28-3 


I otM. mind. 


* '554 Aig. Z+33 


7 38 18-34 


56 53 3*-o 


1 ob«. mirid. 


' ■«?DjLig.Z+i8 


7 38 8-39 


71 5a 386 


1 aba. mirid. 


« aoia Aig. Z-i-39 


7 41 950 


50 4« 34-8 


1 obfl. mirid. 


t Xta Aig. Z+39 


8 I 37-61 


SO 33 *4 4 


1 obB. mirid. 


■ iStx A« Z+as 


8 4 4C-40 


64 37 i8-6 


loba-mirid. 


« qw Air. Z-f 4 


8 3 '4-06 


86 I 511 


I oba. mirid. 


• int A« Z+« 


8 8 iS-87 


68 13 485 


1 obfl. mirid. 


m jmt Ijf. Zt 19 


8 17 44-49 


70 36 1-4 


3oba.mirid. 




340 



Mr. Mamj ObserwMoni qf 



XZZTIL tf 



Observations of OccuHations of Stars by the Moon, 1875, ^9 7 (vf^ 
deduced Equations between the Errors of the Lunar Elements) ; amm 
the Phenomena of Jupiter's Satellites, made at the RadcUffe ObseriKUm 
Oxford ; continued from Vol. XXXV. No. 8, of ihe *' Monthly Notketm 

{Communicated by the Raddiffe Ohstrver.) 



No. 

I 


Day and Year 
of ObeeiTatkm. 

Oct. 24 


Name of Object. 
o'Leonis 


Fhenomenon. }i*iLimU 
Disapp. Bright 


Oxford Haan 
BolarTtma. 
h m a 

'7 31 54*4 


F.:a 


2 


If 


tt 


Beapp. 


Dark 


18 20 32*3 


•• 


3 


Not. 8 


X Aqnarii 


Disapp. 


Dark 


9 *> 45*4 


K 


4 


Dec 9 


19 Arietis 


Disapp. 


Dark 


5 59 465 


K&F.: 


5 


X876. 
Jan. 3 


Lamont 23 


Dtsapp. 


Bright 


738327 


L. 


6 


fi 


tt 


Beapp. 


Bright 


7 40 33-4 


ff 


7 


Feb. 2 


27 Arietis 


Disapp. 


Dark 


6 22 59'4 


K&F.: 


8 


tt 


i» 


Beapp. 


Bright 


7 27 323 


F.K 


9 


March 4 


B.A.C. 2097 


Disapp. 


Dark 


10 54 584 


K 


10 


April I 


47 Gexninomm 


Disapp. 


Dark 


7 «7 71 


L.&F. 


II 


f» 


W.B. (a) Vll. 81, 


2 Disapp. 


Dark 


7 41 377 


L.ftF. 


12 


» 7 


B.A.G. 4225 


Disapp. 


Dark 


8 22 52-9 


L. 


13 


it 


/ Virginis 


Disapp. 


Dark 


II 31 477 


L.&F. 


14 


July 13 


c PiBciam 


Disapp. 


Bright 


13 46-6 


F.B. 


15 


a 


it 


Beapp. 


Dark 


13 54 289 


ff 


16 


„ 16 


23 Tauri 


Disapp. 


Bright 


14 26 51*1 


ff 


17 


it 


24Tauri 


tt 


f» 


14 57 45*4 


ff 


18 


)i 


n Tauri 


tt 


»* 


14 59 17-3 


ff 


19 


» 


23 Tauri 


Beapp. 


Dark 


15 21 171 


ff 


20 


»i 


27 Tauri 


Disapp. 


Bright 


15 33 149 


ff 


21 


»» 


26 Tauri 


i» 


ff 


15 35 1-8 


M 


22 


%i 


28 Tauri 


tt 


tt 


15 35 44 7 


M 


23 


It 


1; Tauri 


Beapp. 


Dark 


15 52 12*1 


f» 


24 


Nov. 29 


47 Arietis 


Disapp. 


Dark 


7 5» »*9 


L.&BE. 


25 


1877. 
Jan. 30 


f> Leonis 


Disapp. 


Bright 


10 45 151 


L. 


>> 


ft 


»» 


tt 


tt 


ID 45 1 58 


H.B. 


26 


n 


It 


Beapp. 


Dark 


II 50 380 


L. 


27 


Feb. 26 


Begulus 


Disapp. 


Dark 


12 39 r8 


L. 


>i 


»» 


If 


>» 


If 


12 39 04 


F.B. 


28 


>» 


>» 


Beapp. 


Bright 


13 44 41 


L. 


if 


fi 


i> 


»» 


>» 


13 44 409 


F.B. 



April 1877. OccuUaUons qf 8iar$ eiCL 341 

Noti$. 

Bo. I. ^ LumiB^ disapp. The star seemed to hang on the Moon's limb for 

3 or 4 seoondfl^ but ultimatelj disappeared instantaneonsly. 

w ^ w reapp. The obserration donbtfol; I turned round to 

Terify mj oonnting, and, on again looking in the telescope, 
the star seemed to reappear at that moment. 

„ 4. 19 Ariitis, disapp. The time noted is that at which I last saw the 

star, which seemed to disappear behind a dense cloud. (K.) 

„ 7. 27 AritHSf disapp. The disappearance was instantaneous and the 

observation good ; the unilluminated disk of the Moon was 
distinctly Tisible. (E.) 

n & tt reapp. At the reappearance the star was faint ; the time 

noted is thou^t to be certainly within 0^*5 ; the Moon's 
motion in N.P.D. was very rapid. (F.B.) 

n 10, II. 47 Oeminorum, disapp., and W.B. (a) VII. 81, 2, disapp. Instan- 
taneous; the unilluminated disk of the Moon distinctly 
▼isible. (F.B.) The BJL. and N.PJ). of W.B. (2) VII. 81. 2 
are obtained from three observations made in 1877. 

n 12. BjLC. 4225, disapp. BoubtAil to a second. 

» 13. / FSrymis, disapp. The star very funt just previous to disappearance. 

(Both observers.) 

11 14. < Piteium, disapp. The star appeared to hang for a few seconds on 

the Moon's limb, and then disappeared behind a projectiozi. 

» 15* M reapp. I am veiy doubtful about this time ; probably too 

late. 

n 17* 24 Tauri, disapp. Faint at disappearance. 

n 18, 20. 9 Tauri, disapp, and 27 Tauri, disapp. At both these phenomena 

the star hung on the Moon's limb for 2*, and overlapped it 
(the colour of the star being plainly distinguished from 
that of the Moon), and then disappeared instantaneously. 

„ 21. 26 Taurit disapp. Star very faint; observation doubtful. 

„ 22. 28 Taurij disapp. Disappearance instantaneous. 

„ 23. 1} Thuri, reapp. The reappearance had taken place at the time noted, 

when I just saw it at the edge of the field of the telescope. 

„ 25. p Tjeoni$, disapp. and reapp. Unsteady ; windy. (L.) 

„ 27. BeguluSy disapp. Disappearance instantaneous. (Both observers.) 



In the following table of the errors of Innar elements result- 
ing from the occoltadons, the Greenwich notation is used, and 
the elements of the Nautical Almanac are nsed uncorrected. All 
the computations have been made bj Mr. Main by the method 
given in his treatise on Spherical and Practical Astronomy. 

The • observations are referred to by the Nos. of reference 
given above. 



I 



Mr. Main, OUerwObm^ 




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April 1877. 



of 8iar$ etc. 



343 



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X 


X 


X 


X 


X 


X 


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1 


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5^ 


s 
.? 


1 


9> 




to 


00 


to 


b 


b 





b 


b 


b 


b 


b 


b 


b 


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1 


1 


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1 


1 


1 


1 


1 


+ 


1 


+ 


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'S 


•s 


•s 


's 


's 


'^ 


"^ 


"^ 


*«s 


"^ 


X 


X 


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X 


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X 


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58 





•8 


3 


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to 

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^ 


to 


& 


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1 


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+ 


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1 


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ro 


s 


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to 


to 

00 


ON 


to 




to 




s 


^^ 


^ 


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s 


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b 


b 


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b 


b 


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• b 


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+ 


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n 





II 


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p\ 


w 


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b 


+ 


+ 


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+ 


+ 


+ 


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+ 


1 






344 



Jfr. Maiih (^ftervoHoM of 
Phemmma of Jwpiter's SateUUes, 



XXXYII. 6y 






nana of 
plMDonwoon. 



Inatnu 
ment. 






•f 



3 
4 

5 

6 
7 



8 



10 



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li 
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ff 



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90 



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n 



1 
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n 

n 

II 

11 

II 

I 

II 
n 
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II 
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Oee. dM»pp- ^^'^ contact lo-foot 
BiMction 
LMtoont 

Ooft.dMapp. Biaection 
Lastcont. 



II 



II 



II 



II 



>f 



KoLdiiapP' 
Shad. V- 



tt 



£cL disapp. 
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fi 



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fi 
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21 III Trs. ingr. 



II 



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II Trs. egp. 



M 
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I. 31 

11 

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II 

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11 



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II 
tt 

tt 
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Last seen 
Last seen 
First oont. 
Last cont 
Last seen 
First seen 
Last oont. 
First seen 
Last oont 
First cont. 
Last cont. 
First cont. 
Last cont. 
First cont 
Bisection 
Last cont 
First cont 
Last cont. 
First cont 
Last cont. 
First cont. 
Bisection 
Last cont 
First cont. 
Last cont 
First cont 
Bisection 
Last cont 
First cont 
Last cont^ 



II 

ti 

It 

II 

II 
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lo-foot 

II 
Heliom. 

It 
lo-foot 

II 
If 
tf 

Holiom. 

tf 

ft 
lo-foot 

ft 
tf 

fl 

Heliom. 
ft 

If 

lo-foot 

tl 
11 
II 

tf 

Heliom. 
fl 



Oxford 
Mean Solar 

Time of 
Obwnration. 

h m • 

o 21 363 I 



Oreenwioh 
Mom Solar n»— »— 

h m a 

K. 



o 23 61 1" 10 31 
o 27 54 



I o o*i| 

I 2 29*7! 



II 7 



2 17 8*1 12 21 55*9 
I 32 217 II 40 



I 41 20'2| 

I 46 59-4) 



II 51 



9 30 33*8 9 35 362 
2 9 23-9\ 



• 12 17 



^ 12 I 



2 14 23-1 
2 8 480 
2 13 27-2 
I 12 39*5 1 
I 17 87) 

I 53 29-3^ 
I 58 28s 
I $2 441 

I 56 135 

1 59 130; 

2 45 327) ^ 

2 58 505' ^^ 

I 39 47o\ 

I 49 154 
I 40 26*4 

I 43 160 

1 46 0*6^ 

2 12 ir7\ 
2 16 41'oJ 

2 3 12*2^ 
2 4 41-9 

2 6 41*6 

2 I 20-5 

2 7 245; 



II 23 



y II 49 



12 26 



y 12 II 



fl 
II 
fl 
fl 

L. 
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fl 

fl 
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L. 

II 
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II 
L. 

If 

fl 

fl 

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11 
fl 
L. 

It 

ft 

ff 

F. B. 

ft 

If 
L. 

It 
L. 

ft 

I* 

F. B. 

If 



Apf3 1877. 



OecuUaUont of 8iar$ dc. 



345 



H 


Hmfmd 

Tcurof 

Ota. 

June I 


• 

\ 

m 


Eel. reftpp. 


Phase of 
FheaomeiKMi. 

••• 


Instrn- 
nMDt. 

Heiom* 


Oxford 
Me«nS(iUr 

Time or 
OtMermtion. 
h m ■ 

9 10. 1*4 


Oreeowich 
Mean 8oUr ^^ . 
Time from "M***- 

h m ■ 

9 16 24s F. B. 


IS 


•« 




I 


Tzs. ingr. 


First oont 


tf 


9 


10 523^ 






tf 








f» 
tf 


n 


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tf 
ff 


9 12 7*1 
9 14 21'8 


9 


18 


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tt 




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n 


tf 


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lo-fbot 


9 


16 9*6^ 






L. 


16 


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I 


Shad. ingr. 


Last oont 


ft 


9 39 iS'^l 






ft 




vt 




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ft 


Bisection 


Heliom. 


9 


36 324 


• 9 39 


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w 




ti 


ft 


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ft 


9 


38 17-2 


. 




tt 


17 


f» 




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lo-lbot 


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17 40^8' 






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tf 


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tf 
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21 451 


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ft 


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ff 


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ft 


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37 53*5 
41 27*0 


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51 


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L. 


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u 


Eel. reapp. 


First seen 


ft 


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ft 




ft 




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tt 


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41 565 


■ II 


48 276 


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ff 


ft 


First seen 


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41 18*1, 






F.B. 


20 


July 


3 


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Bisection 


lo-foot 


10 


57 57-4^ 






L. 




fft 




tt 


ft 


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ft 


II 


7 55-8 






ft 




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10 


51 165 


-II 


10 


F.B. 




t> 




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ti 


Bisection 


ft 


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57 306 






ft 




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ft 


ft 


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ff 


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2 597. 






ft 


21 




14 


m 

tf 


Eel. reapp. 
ft 


First seen 
(Fully seen 


lo-foot 

ft 


9 
9 


3 369 

4 11*8 


9 


12 80 


L. 
ft 


22 


Aug. 


I 


n 


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tt 


9 


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9 


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8 


54 51 


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3 


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ft 


tf 


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tt 


8 


59 203 


ff 


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39 50-9 


8 46 595 


ft 



346 Mr, Main^ OhservaiiotiB etc. xxiYtL 9i 

Notes. 
Ko. 

1 Cloudy. 

2 The satellite rery fkint ; clondj. 

3 The satellite was at least 20* passing into the shadow, which was almoit 

coincident with the limb of the planet. 

4 The shadow was very &int, only seen at intervals, but the time notad is 

supposed to be reiy near the last contact ; windy during the obeerrm- 

tion. 
6 The satellite had been fading in brightness and was ahnoet in oontaet 

with the planet when I last saw it. 
8 Unsteady ; at the last contact the satellite seemed to be on the pUnet and 

to jnmp off again. 

10 The satellite at last contact moved along the limb of the planet for more 

than half an hour, the two limbs being in contact at 13^ 21* ; I did not 
think to look for the shadow till that time, when I was surprised to find it 
folly on the disk of the planet, with the limb just in contact. I thought 
every minute the satellite was coming off the planet, but on referring 
to the Nautical Almanac I found it would not do so for nearly tvo 
hours. Too tired to wait for the egress. 

11 Uncertain. (L.) 

The image of the planet very diffused. (F.B.) 

12 Very doubtful. (L.) 

13 Definition very bad. (L.) 

14 Reappearance instantaneous. 

16 Shadow veiy faint ; probably the time noted is one minute too late. (L.) 
The last contact is considered satisfactory. The times noted have been 

each diminished by five minutes. (F.B.) 

17 The planet ill-defined ; the satellite very faint. (Both observers.) 

19 Very faint at reappearance. (L.) 

Reappearance instantaneous, bat the satellite faint owing to cloud. (F.K) 

20 Very unsteady and ill-dofined; the satellite hung on the limb for some 

minutes after the last contact appeared to have taken place. (L.) 
The planet was very tremulous, and the satellite seemed to hang on the 
limb for some minutes after last contact ; at 11^ 12" the satellite was 
quite detached from the limb. (F.B.) 
22 The satellite faint. 

24 Unsteady. 

25 Cloudy daring the observation ; the planet was very badly defined and 

unsteady ; the satellite seemed to jump away from it after the contact 
had taken place. 

26 Cloudy during the observation ; the ratellite was very faint at the time 

of reappearance, and did not attain its usual brightness till one minute 

after. 
The initials L., K., F.B., H.B. are those of Mr. Lucas, Mr. Keating; Mr. F, 

Bellamy* and Mr. H. Bellamy. 
The instruments used were the helioraet-er with power of 200, and the lo-foot 

telescope with power uf 160. 

April 3. 1S77. 



kpni 1877. Mr, Perry, The Planei Vulcan. 347 



The Planet Vulcan. By the Rev. S. J. Perry. 

The weather yn^ exceedingly fayonrable here for the search 
for the intermercarial planet, and a careful watch was main- 
tained thronghont the whole of the 21st, 22nd, and 23rd of 
Jfarch. The spider-line micrometer was used with the 8-inch 
achTomatio, ana the Son's image, projected on a screen of very 
imooth white cardboard attached to the eye-end of the tele- 
aoope, had a diameter of ^ inches. An excellent driving clock 
is attached to the Eqnatoreal. On the 21st of March the San 
was obseryed from 9.30 a.m. till 6.3 p.m. G.M.T. Passing clonds 
obscDred the image 

m h m h m 

twice for 10 beginning Ht 2 49 and at 5 40 

twice „ 15 „ „ II 31 ♦, „ 3 > 

once „ 23 „ „ 12 25 

On March 22 the watch was kept up from 7.0 a.m. till 
6. CO P.M., with only five breaks of continuity, viz. for 

m h m 

12 beginning at 10 34 

14 .» » " 48 

17 M M 10 5 

20 „ ,,28 

and 24 M » 12 25 

On March 23, from 7.30 a.m. till i p.m., there wa.s no inter- 
ruption, bnt the Snn was obscured from i p.m. till 2** 27™. Clouds 
^ interfered for 



m 
10 


beginning 


at 


h 
3 


m 
10 


II 


>> 


>» 


2 


37 


16 


»» 


»» 


3 


42 



Observations were discontinued at 5.10 p.m. on account of 
^"0 indistinctness of the image. 

I have given above only the times when the Sun was ob- 
•^^^^i^ for at least 10™; other lesser interruptions from small 
P^^g clouds were accurately noted, but it does not seem 
^*®oegiry to reproduce them here. 

The aefinition on all three days was generally very good, and 
^ atmosphere quite steady euough for good micrometric 
^^^arements. The faculsB around the double group of eight or 
^e spots on the western limb of the Sun, and the vast group 
^^ facnlffi without any accompanying spot on the eastern side, 
^ere the only features that broke the monotony of the mottled 
•orface during the whole period of observation. 

D D 



348 Mr. Gaproiiy The Planet Vuhan, XXXYll. 6, 

These observations, combined with any other set taken under 
equally favourable circnmstances in this country, would sufBoe 
to establish the fact that Vulcan did not pass across the aolar 
disk whilst the Sun was above oar horizon from the 21 at to the 
23rd of March 1877. 

Stomyhurst Observatortf^ 
iSyj, March 24. 



R'Cport of Examinalion of the Swris Disk at Ouildoum, OuUdford, on 
2i8f, 22nd., and 2^rd March 1877, for the siupected pUmet 
Vulcan^ with a 3^-1^. Cooke Refractor, Huyghenian ey&fneoet 
20 and 50. Transit eye-pi^ce about 40. By J. Band Gapron, 
Esq. 

Wednesday, 21/?/ March 1877. 

9 to 10. Frequent examinations. Sun spot, with group of 

much smaller ones, well seen near edge of Sun. 
I o to 2 . Very cloudy, occasional glimpses of Sun's disk through 

clouds. 
2 to 4. Brighter, but still cloudy, allowing of examinations 

from time to time; practised photo- plates with 

larger telescope (8^-inch reflector). 

Thursday, 22nd March. 

7.10. Sunrise in mist; small spot and facalse seen on Sun's 

edge. 
7.41. Less mist; spot plainer. 
7.54. Mist breaking; Sun*s limb sharp; spot and faculsB very 

distinct. 
8.26. Still misty, but spot and faculsB well defined. 

9.1. \ 
9.33. Sun getting above mist, with bright disk. 
10.12. / 

10.47. Light misty clouds, but spot well seen, 
ii.o. 



11.35 



Sun quite bright. 

Four Kennett plates taken between 9.30 and 11.30 with 
reflector. 
11.52. Sun clouded. 
12.20. Kennett plate, No. 5. 

1 2.50. Snow flakes seen crossing the Sun's disk ; none fell below. 
12.57. Snowdrift continued, and clouds came up. 
2.26. Curious cloud shadows overhead. 
2.39. Run's reappearance with bright disk. 



ipril 1877. Mr. Denning, Badiant Points etc, 349 

j^6. Kennett plate, No. 6. \ 

^.51. Ditto „ 7. I Small spot very close to Sqq'b 

3.30. Ditto ,, 8. 1 edge. 

3.34. Ditto „ 9. ) 

Clonds and mist then came on. 
^ . :25. Sun low ; disk clear. 

Friday y 23rd March. 

^ . 58. \ 
-^•28. 

^^' Sharp frost ; Son rose in slight mist, which afterwards 
^ 2i I fS9^ denser ; disk, however, well seen and quite dear. 

X0.0. ^ 

^^•18. Misty ; fine San halo. 

*^-3o. Disk clear. 

^ I.e. Mist ; wind freshening. 

1 1.7. Disk clear. 

^ 1-38. Mist and wind ; clonds coming np. 

' '-50. Clearer again. 

'^'33- Bright gleam ; disk well seen and quite pure. 

i.o. Glimpse among clouds, 

'•45. Same. 

'•48. Very bright glimpse. 

^•53. Disk well seen through mist. 

i-'^.S. Same (with 20). 

4-4.0. Sun in cloud and mist, hut disk fairly seen with 20 ; wind 

high. 

5- z o. Fine Sun halo and Sun set in clouds. 



Chiil4fard, 
AfTil 4. 1877. 



^^ciiaiU PeinU of Shooting Stan. From Captain Tupman^s 

unreduced Observations 1869-71. 

By W. F. Denning, Esq., F.M.S. 

{CommunieaUd by A. C Ranyard^ Esq., M.A.) 

The valuable observations of Shooting Stars by Captain 

^^pman in the years 1869-70-71, printed in 1873 ^^^ *'^® 

^^tish Association, contain a considerable number of meteor- 

Pjjjilhs that have not hitherto been reduced to their radiant points. 

^UB, between Jan. 21 -Feb. 23 (1869) there are about 135, 

^^^tween Sept. 6-Oct. 13 (1869-71) 130, and between Dec. 12-23 

(chiefly in 1869) 40 more, making about 300 altojrether. These 

D D 2 



35® ^'"'^ Denning, Radiant FoUvts xxrvii. 6, 

I have projected upon an 1 8-inch globe, and traced their several 
radiant centres, as specified in the subjoined list of 20 snch 
positions well-ascertained, and supplementary list of 8 others 
less certainly indicated. I have annexed the positions of other 
observers which they confirm, and the comparison shows that 
there is a very fair accordance in most cases. It should be 
mentioned that these new determinations are purely independent 
of and separate from Captain Tupman's older positions (Monthly 
Notices, vol. xxxiii. p. 300), having been deduced from other 
meteors seen on other nights ; in fact, they are founded on dif- 
ferent materials, though gathered by the same hand, and the 
two sets of positions compared together in the table, each 
possess a distinct value, whether confirmatory or otherwise. The 
chief shower in the new list is No. 2 at a 236^ ^+11^ (near a 
Serpentis) for Jan. 21-Peb. 23, which this year I confirmed in 
the same place, and was well observed by Captain Tupman 
Feb, 13, 1869, at 237** +13**. Nos. 11 and 16 were also active 
radiants. No. 13 (Sept.) at 105*" +5 3** is not included in existing 
catalogues, though I found a position at 90^ +58° for Oct. 
(No. 29 of my list [1876] of radiants, Monthly Notices, vol. 
XXX vii. p. 105). The average of the two comes out at 98** +5 6% 
which is sueipiciously near the radiant point of Donati's 
Comet (100® +59° Sept. 8) as computed by Professor Herschel 
(see B.A. Report, 1875, p. 233)*. Capt. Tupman describes the 
. meteora as ** very swift," and I find ms estimate of the appa. 
rent velocity of 9 of them averaged o'2 sec. for 10 degrees. 
I found them bright and rapid, leaving streaks. The fourth 
radiant in the supplementary list verifies a new and prominent 
shower I saw from near ;// Oygni in January last, and since con- 
firmed by Prof. Heisat 297^ + 53° Jan. 1-2 1. 

The shooting stars employed in the determination of these 
radiants do not include the whole of Capt. Tupman's unreduced 
paths. Between Nov. 3-12, 1869, there are 80 such observations, 
and in August 1870 a few more ; but I have not gone over them, 
inasmuch as the chief systems (Leonids and Tattncb in the former, 
and Ferseids and Gassiop&ids in the latter) common to those 
periods are already thoroughly well known by the able investi- 
gations of Mr. Greg and Prof. Herschel, of the British Asso- 
ciation Luminous Meteor Committee. 

* Since the above was written, I have examined many hundreds of meteor- 
paths reeorded between Aug. 15-Oct. 15 by Capt. Tupman, Mr. Lucas (Badcliffe 
Obseryatory, Oxford), the Italian observers (Schiaparelli, Denza, and others, 
1872), and myself, and found 33 meteors agreeing to a radiant at 99° + 57^ 
for September 1-15 ; while for the whole two months I have douMe that 
number fiK)m a general centre at loi^ -1- 57^. The accordance of this new 
shower in date and position with the nodal passage of Donati's Comet is 
remarkable, though possibly accidental and showing no real affinity of origin. 
— W. F. D. 



1877. 



of Shooting Sturg, 1869-71. 



35^ 




VO 






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to 



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M fc« <^VO to >mO\r\mmmm\f\\r\t^f^ 

mm mm mm mmmmmmmmm^mmmm^mmm 



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1 - ro »0 



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k>4 ^*'oD •^w*o^»osor^coo. O "^ M fO^tOVO »^ 00 



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(ifgoiqo) i^ -400 o* 9 '^<^®S 



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Mr. Denning^ Radiant Poinii etc. uulth. < 






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April 1877. Copt. Tupman, Meteor of March 17. 353 



The Oreai Meteor of 1877, March 17. By Capt. G. L. Tupman. 

A few minutes before 10 o'clock, G.M.T., on the evening of 
March 17, a meteor of very exceptional brilliancy was observed 
from the southern and western counties. 

At Frome, 51? 14' N., 2® 24' W., it was seen by the Rev. G. 
Homer to begin 3^ N. of PoUux, and terminate between y and r 
Persei, 

At Cambridge, 52* 13' N., o** 6' E., Mr. A. P. Trotter observed 
that its path and the Ime joining c and t Orionis bisected each 
other, the path being about twice as long as Orion's belt. 

At Blensin^n, 51** 30' N., o'' 12' W., Mr. W. Thackeray saw 
it shoot from e Orionis^ downwards to the right, at an angle of 37^ 
to the horizon. 

At Gunnersbury, 51° 29' N., o® 17' W., it appeared to come 
from Oemini, to pass over Aldeharan, and disappear below the 
Pleiades (Nature, Mfrch 22). 

At Tetburv, si** 38' N., 2** 9' W., Mr. E. C. Davis saw it disap- 
pear close to the Pleiades. Its path was inclined about 45° to 
the horizon, downwards and to the right. 

At Boesall, 53** 55' N., 3° 3' W., it appeared to move from 3** 
north-west of a Hydrce to a point in R.A. 7^* 30"*, Decl. 20® S. 
(Nature, March 29, and April 5). 

At Brighton, 50** 49' N., o*» 8' W., Mr. W. Ainslie Hollis saw 
it disappear between the belt and the Pleiades, after describing 
a path of about 15^ 

From these observations the radiant must have been very near 
R.A. 145®, N.P.D. 95°, or due south, at an altitude of 34®. 

The point of disappearance is pretty accurately obtained at 29 
statute miles over 5° 41' N., 3® 4' W. (near Pontypool). Com- 
bining, then, the Fronie, Rossall, and Cambridge observations, 
as the most precise, the meteor first became visible 60 statute 
miles over 50® 59' N., 3° 4' W., or nearly over Taunton. This path 
satisfies the other descriptions within ordinary errors of observa- 
tion. Its length was 59 statute miles. The duration was given as 
certainly about 3* by Mr. Homer ; 3' by the observer at Gunners- 
bnry ; 4* or 5* by Mr. Hollis ; 3' by Mr. Ballard, at Banbury ; and 
2" by another observer. The mean of these is 3'*i, giving a rela- 
tive velocity of 19 miles per second. 

From the radiant point given above, the following parabolic 
elements of its orbit are deduced : — 

o 
Q 177-4 

I 8-5 

w 2225 

q 850 

Motion Direct 



)54 Trof, PrUehard^ Two Mechanical xxxvii. 6, 

whence the relative yelocitj is i3'3 statute miles per second, 
and the total duration ^\ seconds. 

The size of the meteor was described as one-sixth the diameter 
of the Moon, at Banbnrj, and also at Brighton, and one-half at 
Bristol, bnt doubtless this large size was chiefly due to irradia- 
tion. 

During the first half of its track, the meteor was like burning 
magnesium in appearance, then the colour became red, and lastly 
was vivid green. All along its track fiery ashes fell towards the 
Earth, and after the eztiuction of the principal part, a body of 
dark red sparks continued to fall for a short distance, as seen at 
Tetbury by Mr. Davis. Lady Portsmouth, driving near Basing- 
stoke, 90 miles from the meteor, and facing west, *' was startled 
by what appeared to be blue or bluish.green lights falliug ap- 
parently in large flakes into a field on her left. Some seconds 
after, while the whole country was lighted up as if by the 
brightest possible lightning, a large red ball was seen travelling 
with comparative slowness on the right, over a field, into which 
it appeared to fall." From Waterford the meteor was seen to be 
double, one part closely following the other. This duplicity is 
not reported from any other place. 

The meteor left little or no streak, and did not detonate, for 
several of the observers state that they listened for any noise. 

The average of all the recorded times is 9** 57" G.M.T. 

In Mr. Greg*s List of Meteoric Radiants for 1874, No. 15 is 
R.A. 143°, N.P.D. 97®, from January 3 to March 16 (?). Such 
a radiant would be nearly stationary for a long time, as the meteors 
overtake the Earth obliquely ; its duration to March 1 7 is there- 
fore confirmed. 

A curious instance of the inaccuracy with which meteor 
tracks are sometimes described is that of "J. M. W." in the 
Times, who says that " in London the meteor was two-thirds the 
size of the Moon when overhead^ As a matter of fact, it was 
never within 65° of the zenith of London. 



Two Mechanical Sohdiona of Kepler's Problem. 
By Prof. C. Pritchard. 

It is unnecessary to dilate upon the boon which would be 
conferred on observatories and computers, if the tiresomeness of 
the solution of this problem can be diminished. Every skilful 
computer has no doubt his own peculiar method, which to him 
by habit facilitates the work more or less; perhaps that proposed 
by Dr. de Gasparis in the last Number of the Monthly Notices 
will be among the best. I venture to submit to the Society two 
mechanical methods of solution, which in the course of less than 
two minut<^s landed mo just at the point reached in the ex- 



April 1S77. ScluUotis of Kepler* a Prohlem, 355 

ample given by Dr. de GkuBparis above. The principlo is as 
foIlowB; bat the description, if fall, woald occapy more time than 
tiie practical working of an actoal case. Soppose a lath AB 
(fig. i) divided into inches and tenths, and that two trammels 
slide npon it, accaratelj fitted. Each inch is intended to 
represent the length of an arc of a circle of one degree, the 
radios of which, therefore, is 57*296 inches. This subdivision 
into tenths is eqaivalent to one hand red th of an inch by estima- 
tion, and admitting of no error of that amoant, i.e. no error 
amoontinff to $6'\ The other implement required is a good 
carpenter^ rale (fig 2) with a good hinge, with a line on each of 
the two laths, diverging from the middle of the hinge as the 
origin, and each line divided into the line of natural sines OC, 
OD to one tenth of a degree, and to the same radius as the lath. 
This implement forms, in fact, what is technically called a sector. 
Sappoee the question were : " Having given M, the mean 
anomaly^ s 15*^*676, and the eccentricity e='5, required the 
eooentric anomaly ti." 

The well-known form is i4 = M -f e sin 14. 

Inasmuch as the sine of 30^ is one-half of the radius, open 
the two leffs of the jointed rule, or sector, until from 30° to 30° 
roans *5 x sm 30^, or one-fourth of 5 7 296 inches, i.e. 14*324 inches. 
It follows from the construction that, in the sector thus opened, 
from 10^ to 10** will span J sin 10®, and from 20° to 20®, J sin 20° 
Ao^ and so on for all corresponding divisions of the two lines of 
natural sines. The sector being thas prepared, take the divided 
lath and set one trammel (A) at the mean anomaly 15*68 
inches, and let the other trammel (B) be moved backwards and 
forwards until a division (u) is found on it, such that from A 
to B will span across the space between the same identical 
divisions u to n on the opened sector; u° is then the 
eccentric anomaly sought. In this example u° turns out to be 
30® quam proxime. 

The reading of this description of the modus operaiidi has 
probably occupied more time than the working of an actual 
instance when once understood. The truth also of the method 
is obvious. For, from O to A on the lath is made to equal the mean 
anomaly, and from A to B, found as above, is e sin n ; conse- 
quently from O to B, i.e. the reading of B on the divided lath, is 
OA-f AB = M + e sin u ^ «. 

Practically, my own implements are, for convenience, con- 
structed with a radius of 20 inches, and as these land us at once 
within I '"5 of the true value of ti, it is quite near enough for the 
application of the differential formula, finally completing the 
value of u. Of course, if the scales were absolutely divided, and 
could be so read, the solution above obtained would be strictly 
accurate. But supposing the reading thus obtained to be Uq, and 
the correct value t*o+^^> then 

, M + ^ sin w,— M« 
ou — — • 

I — C cos W, 



356 



Prof, PritcJiard, Two Mecfianical xxxvii. 6, 



Fi^ ,3 . 




Fi a . 4f 




Fi Q.l 



A B 

Ol I I I I I I P uM I I I 



\^^ A ' I *~-H^ B ff"^^ '^~^ 



t il l 



JS'6S 



SO 



Fi <f,2 . 



90. 



P 






{)' 







.•in, 

^7/ 






\ 


."' "' 






10 

1 


20 





u // 



r^ AB 



."0 



00 

J _ 



nn 



c 



April i877- Solutions of Kepler* $ Problem. 357 

I will merely add that it is obvious that the length of the 
divided lath may be considerably curtailed in practioe by a doable 
fmmbering of the divisions, the apper nnmbering commencing 
(say) at 80^ and proceeding to 180**, and the lower commencing 
wiui o^ and proceeding to 90*^. 

Other minor conveniences will suggest themselves to any 
computer of ingenuity, and the author of this paper will be 
happy to give any further assistance or description required. 

JEiesides the preceding method, I have completed another con- 
trivance, which is, perhaps, equally effective, and even somewhat 
easier to use, inasmuch as there is nothing tentative in its appli- 
cation. The g^rm of the thought will be found in the Monthly 
Notieee a few years back, where Mr. Proctor refers to a method 
proposed by Prof. Adams, and which he there elaborates at some 
length, but which practically cannot well be utilised in computa- 
tions. (See Monthly Notices, April 1873.) 

The machine as used in the Oxford IJni varsity Observatory 
is as follows : — 

On a flat board is carefully stretched a sheet of paper, divided 
into squares of one inch, and subdivided again into squares of 
twentieths or thirtieths of inches. 

This pKper (or others like it) is supplied by Messrs. Waterlow, 
of Birchin Lane, London, and no doubt can be procured elsewhere. 

From A to B is 45 inches (fig. 3), divided into 180 equal 
parts by means of the engraved lines. Each inch represents 
four degrees. 

On this as base is erected the curve of sines so that CD, the 
sine of 90°, is equal to the radius, i.e. to the length of the arc 
of S7**'296, or 14324 inches. DE is taken = 10 inches, and EF, 
perpendicular to it, is also 10 inches, divided by the engraved 
lines into twentieths of an inch. Below AB is a groove, KL, 
strictly parallel to the base AB. Into this groove is placed the 
slider PQ (fie. 4) carrying at its middle a thin lath with a per- 
fectly straight bevelled edge, ROS, which, by means of a 
thumbscrew, moves round O, and can be thereby fixed at any 
inclination to PQ. The curvilinear part ADB is numbered 
correspondingly to the base ACD for every 10 degrees, and is 
capable of being read, by means of the engraved lines and esti- 
mation of subdivisions, to 2' of arc. 

The application of this simple implement to an actual ex- 
ample is easy and rapid. 

For instance, let the mean anomaly M = i24°'933, e ='875, 
and let it be required to find the eccentric anomaly U. For this 
purpose place the slide in the grroove, and move the lath round 
until the straightedge passes precisely against D and G, 
where the reading of G on the small scale EF is the eccentricity 
— here = 875 inches. Then clamp the lath by means of the 
thumbscrew ; and slide it until its edge stands precisely 
against the mean anomaly M on the base, where the reading is 
here i24°'933 as near as estimation admits. Then the reading 



35 3 Mr. Neiaon^ On tJie Inetjtiality eU. xxx?u. 6, 

U, where the straightedge cats the line of sines, is the eccentric 
anomaly songht. In this instance U reads 150*^ qxuim yroxime, 
bat probably not exactly. Whatever the reading is, it can be 
treated in the asaal way as a close approximate solation ; and 
from it exactness to any amoant of .precision may be obtained 
by the application of the differential formala above. It will be 
observed that the only novelty here claimed consists in the appli- 
cation of the slider in the groove, thas obviating any drawing 
of parallel lines ; and in the adaptation of the small scale EF, 
thns famishing an immediate means of placing the straightedge 
at the proper inclination to the base ACB required by the 
eccentricity e. 

This machine admits of home manufacture: and either oi 
the two solves the question of Kepler's Problem with sufficient 
accuracy for double-star orbits without farther computation. 

The demonstration is obvious. For 



hence 
that is 



Mtt = Uw.cot DGE Bs pjT'Utt « e sin A«; 



Att ^ AM 4- Mii = M + e sin An. 
eU ■= M + c sin U. 



On the Inec[uality in the Mooti's Longitude discovered by 

Prof. Newcomh. By E. Neison, Esq. 

In my communication to the Society entitled ** On the 
Lunar Perturbations arising from the Planet Jupiter " (Monthly 
Notices, XXX vii p. 248), reference was made to anew periodical 
term in the Moon's Longitude of the form 

Ji; = -i"-i63sin{(2-2w,-c)n<+/-2/; + A}, 

where (nt -f/) denotes the mean longitude of tlie Moon, 
(cwf+/— A) is the mean anomaly of the Moon, and (w*|W<-f/,) 
represents the mean longitude of Jupiter. Reducing the argu- 
ment of this term to a form depending on the mean anomaly of 
the Moon (=^7) and a term increasing directly with the time, 
it becomes 

8t; - - r'-i63 sin {i/'+ 20°-85 (Y- 185576)}, 

or, what is the same thing, 

«i; = + r'163 sin {fjf + 20°'Ss (¥-1864-4)1. 

In his communication to the Society, ** On a hitherto unnoticed 
Inequality in the Longitude of the Moon " (Monthly Noticegy 
June 1876, p. 358), Prof. Newcomb describes a new empirical 
term discovered by himself, and which is 

iu= -r'-5sin{^ + N°-90°}, 



April 1877. Trof, Wiwnttke^ Comet 1877, II. 359 

N - i63<>-2 + 2i<> 6 {/- 1868 5). 

Bednoing this to the same form as the theoretical term, it 
bscomes 

Zo^ -r-Siinly + aio-eCY- 18651)}. 

The two terms are therefore identical, with the exception of 
Prof. Newoomb's empirical term having the greater coefficient. 

This fikct entirely confirms the discovery made by Prof. 
Niewoomby and is obvionsly entirely anaffectea by the existence 
of any discrepancy between the corrections to Hansen's Tables 
deduced by Prof. Newcomb and the observed corrections snch 
M Cmpt, Tapman has made ont. 

Owing to an accidental error, which has jnst been detected, 
towards the end of the numerical redaction of the analytical 
results, the values of the co-efficients of the ineqaalities due to 
Jupiter given in the March number of the Monthly Notices are 
not quite accurate. They should be 



And 



«i a -o"-578coe{(2-2m,- c)fi<+/-2/,+ A} 
— o"-oo3 cos {(2 — 2/n, — 2c)nt - 2/, + 2A} , 



80 « —i"- 163 Bin {(2-2^1— c)tit+f—2/i+ A] 
+ 2"'200 sin { (2 — 2WI, — 2c)nt — 2/, + 2 A } . 



Comet 1877, 27., disc^yvered by Frofessor Winnecke April 5. 
{Extract of a Letter from Prof. Winnecke to Mr. Hind). 

" The new CJomet was observed here by me on April 5, 6, 
and 7. From these observations Herr Hartwig has calculated 
the orbital elements : — 

T April 181741 Berlin Time. 



It 



ir-a 


65 51 21 


Q 


317 SI 18 (18770) 


• 

t 


123 17 18 


log 5 


996767 



For the middle observation A\ =-f 2''*o, A/3 = — 10' -o (C — O). 
** Prom these elements Dr. Schnr has deduced the following 
Ephemeris : — 



360 Trof, PrUchardf Comets of 1877. xxxvii. 6, 



12* Berlin 
April 5 


R.A. 
h m 8 
22 7 42 


8 

/ 

+ 14 41*9 


logr 
9*9802 


log A 
01458 


»> 9 


22 10 56 


19 33 I 


99736 


0*1149 


» 13 


22 15 5 


25 8-9 


99694 


0*0831 


M 17 


22 20 34 


31 364 


99677 


00518 


*i 21 


22 28 II 


39 00 


99686 


00226 


,. 25 


22 39 20 


47 18-5 


99719 


99982 


» 29 


22 56 53 


56 194 


99777 


9-9812 


May 3 


23 27 48 


65 33 2 


9-9857 


99742 


M 7 


31 40 


+ 74 0-3 


9*9955 


99783 



" The analogy of these elements with those of the Comets 
1827 II. and 1852 II. is great, and the circumstance of the 
intervals being nearly equal gives it a certain significance." 



The Gomeis of 1877. By Professor C. Pritchard. 

Borelly*8 Comet I. 

The Ephemeris of Borelly's Comet was sent to me at the 
Oxford University, by the Astronomer Boyal, on the 20th of 
February, and was observed here on the same night. Snb- 
sequentlj to this it has been observed 14 times, and of these 
observations nine are completely reduced; the remaining six 
await the co-ordinates of the comparison stars, which have been 
kindly promised by the Astronomer Royal. When this tele- 
scopic comet was first seen in our large refractor of 12^ inches 
aperture it appeared to be suflSciently bright for observation 
with an aperture of probably 3 inches, and was, I believe, 
actually observed by Captain Tupman, at the Royal Observatory, 
with a telescope of that aperture. On the 30th March the comet 
was observed for the last time in our great telescope with con- 
siderable difficulty ; on the 4th April it was too faint to be cer- 
tainly seen in our instrument, and it is now probably out of 
sight. The whole series of observations will be presented to the 
Society as soon as the reduction is complete. 

jy Arrest^ Comet. 

D' Arrest's Comet has here been looked for in vain, in the places 
assigned for it in Leveau's Ephemeris. The twilight and the 
Moon may render observations of this interesting body very 
difficult for some time to come. 

Winnecke's Comet II. 

From an observation made on the 5th of this month at 
Strasbnrg, and telegraphed to this Observatory by the Astro- 



Apd 1877. Trof. Priichard, Oameis of 1877. 361 

^^omet Royal, tog^thei* with two observations made here on the 
^hta of the 7th and nth inst., the following preliminary 
^^Bments and Ephemeris have been computed : — 

T » April 19*98193 G.M.T. 



If 



■ Apparent Equinox, Ap. 7. 



W a 250 48 27 

Q » 318 2 21 
t = 57 55 2 

logv = 9*974^138 

Motion retrograde. 

Ephemeris for Greenwich Mean Midnight. 

R.A. i log A 



h m 

April 12 22 14- 1 +23 29 

13 22 153 24 55 

14 22 i6'5 26 24 

15 22 17-8 27 56 

16 22 19*2 29 31 

17 22 207 31 9 

18 22 22-3 32 51 



01024 



00869 



0*0717 



0*0568 




19 22 241 34 36 

20 22 260 36 25 0*0425 

This oomet as first seen here on the 7th inst. was tolerably 

ipicaons, with considerable condensation, approaching to a 

letary nnclens, the whole nebalaritj, in early twilight, having 

diameter of aboat a minate and a half. On the iith inst., 

^^ .ithont apparent alteration in form or brightness, it was dis- 

^^inctly visible in a 2 -inch telescope, and from the character of 

^^t8 orbit may probably become visible to the naked eye about 

"ihe end of the month. 

1877, 4p"' 13- 

P.S. — Snbseqaently to the reading of this paper another 
Comet was discovered by Mr. Swift, of Rochester, U.S., on 
Avnl II, and, independently, on April 14, by M. Borelly, at 
Uarseilles, in the Constellation Cassiopeia. This Comet was 
observed here on the i6th, and on every favourable opportunity 
since. The observations will in due course be communicated to 
the Society. 



362 The Johnson Memorial Priue. XXXVIL 6, 

Note on a Deviation of the Plumhline, By M. Otto Stmye. 

It maj be interesting to mention that eztraordinaiy deriik- 
tions of the plnmbline have been discovered in the Crimea by M. 
Kortazzi, Director of the Observatory, Nicolayeff. Fop lEVJta, 
A^ = + 29", AX = —28" ; for Sevastopol, A^ = +5", AX = +21". 
We are about to examine the matter accurately. As Falta has 
been a successfal Venus station, the deviation may possibly affect 
the future computation of its parallax. Of course the geodetic 
co-ordinates should be used as deduced from undisturbed points, 
together with Greenwich time of transit corresponding to the 
deviated plnmbline. 
10/A March 1877. 



The Johnson Memorial Prize. 

(Extracted from the Oaford University Gasette of Jannaiy 23, 1877.) 

The Trustees of the Johnson Memorial Prize for the en- 
couragement of the study of Astronomy and Meteorology 
propose the following subject for an essay : — 

The History of the Successive Stages of our Knowledge of NehuUB^ 
Nebulous Stars, and Star GlxCsiers, from the time of Sir 
William Herschel. 

The prize is open to all members of the University of Oxford, 
and consists of a gold medal of the value of ten guineas, 
together with so much of the dividends for four years on 338Z. 
Reduced Annuities as shall remain after the cost of the medal 
and other expenses have been defrayed. 

Candidates are to send their essays to the Registrar of the 
University, under a sealed cover marked ' Johnson Memorial Prize 
Essay,' on or before March 31, 1879, each candidate concealing 
his name, distinguishing his essay by a motto, and sending at the 
same time his name sealed up under cover with the same motto 
written upon it. 



Correction. — Monthly NoiiceSy vol. iii. p. 205, Feb. 1877. — 
An error of some magnitude in the ** Report on the Progress of 
Meteoric Astronomy *' (four last lines and the note att he bottom 
of the page) requires to be corrected. The date there given of 
an aerolite said to have fallen at Louisville, Kentucky, U.S., on 
the 8th, should have been on the i8th of July 1876. No co- 
incidence of the date accordingly occurred (such as is mentioned 
in the note at that place) with that of the large meteor seen in 
Indiana, U.S., on the 8th July 1876. 



MONTHLY NOTICES 

OP THE 

ROYAL ASTRONOMICAL SOCIETY. 

Vol. XXXVII. Mag 1 1, 1877. No. 7. 

William Huogins, Esq., F.R.S., President, in the Chair. 

William Morris Beaufort, Esq., 18 Piccadilly, and AthensBnm 
Club, 

balloted for and dnlj elected a Fellow of the Society. 



ExtracU from Letters received hy the Astronomer BoycUj relating to 
the Search for the supposed Intro-Mercurial Planet, 

The post has now brought letters in replj to some of the 
telegrams which were addressed to distant stations requesting a 
search for the supposed Intra- Mercurial Planet. The following 
is the substance of the information conveyed. 

From B. N, Pogson, Esq., Government Observatory, Madras, 

" Eye-observations were made at nearly every ten minutes 
on March 21, 22, 23, and fourteen photographs were taken on 
March 22. Vvlcan was not seen." 

From Charles Todd, Esq., General Post Office, Adelaide, 

" The weather was excessively bad, with clouds and thunder- 
storm ; 3-| inches of rain fell in Adelaide, and 5 or 6 inches in 
the neighbourhood. Observations wore attempted, but Vulcan 
was not seen." 

From B, L. J, Ellery, Esq,, The Observatory, Afelbmime, 

** The weather was fine, the Sun was observed almost un- 
interruptedly, and numerous photographs were taken. No ap- 
pearance of Vulcan,** 

Royal Observatory, Greenwich, 
1877, Aj^ 7. 

E E 



364 Sun Spot Drawings of the Rev. Frederick Howlett. XXXYU. 7, 



Sim Spot Drawings of the Rev. Frederick Howlett. 

In the short account given in the May number of the 
Monthly Notices for 1876 of the volumes of Sun Spot Drawings 
which have been presented to the Library of the Astronomical 
Society by the Rev. F. Howlett, it should have been mentioned that 
a large number of the drawings of the Sun's disk are marked with 
a small line and figures, indicating the distance of the west point 
of the Sun's limb :^m the vertex or highest point of the Son 
above the horizon at the time of observation. 

The image of the Sun was projected on a screen on which 
was a graduated circle with 0° at the vortex, 90° being to the 
right hand, 180° at the bottom, and 270*^ to the lefb hand. A 
small spot, or some easily recogpiised detail of an irregular largo 
spot or large group, was brought to the centre of the graduated 
circle, which was marked by a small pin-hole in the cardboard 
screen. The telescope was then left in position, and as the 
Sun's image was carried off the screen by the Earth's motion, 
the angular distance from the vertex at which the spot or detail 
which had been brought to the centre passed across tho circum- 
ference of the graduated circle was noted and entered upon tho 
drawing. The position of a small line which has been marked 
upon the edge of the drawings of the Sun's disk depends on the 
assumption, that the highest point upon the page of the book 
accurately corresponded with the highest point of the Sun's 
image as seen by projection on the screen. 

The horizontal and vertical co-ordinates of spots given in 
some of the drawings were made with an eye-piece in the focus 
of which was a thin slip of semi-transparent mother-of-pearl, 
graduated into divisions yiij^^ ^^ *^ ^'^ch apart, every 5th and 
loth gradation being made more conspicuous for the purpose 
of easily counting them. At right angles to tho scale, and 
nearly bisecting the field of view, was stretched a fine wire, 
which was first placed vertically, so as to bisect the image of tho 
Sun ; the mother-of-pearl scale was now brought up to tho 
centre of the spot, and the number of gradations to the riji^ht or 
left of the wire were counted ; the eye-piece was then turned so 
that the wire when in a horizontal position bisected the Sun's 
image, and the mother-of-pearl scale brought again to the spot, 
and the number of gradations above or below the wire counted 
as before. It will be seen that these distances do not correspond 
to the horizontal and vertical ordinates of PastorflTs drawings, 
in which the distances measured horizontally and vertically were 
measured from the limbs of the Sun. 



May 1877. Padre Secchi, Note on alleged Fall of an Aerolite. 365 

Note on the alleged Fall of an Aerolite at Supino, Italy, 

By Padre Secchi. 

(From a Letter to E, Dunkin, Esq., F.R.8,) 

In the Monthly Notices j vol. xxxvii., No. 4, February 1877, 
page 205, I find indicated a fall of a meteor on September 4, 1875, 
4 P.M. local time, at Sapino, near Rome, in the province of 
?ronnone. As I am well acquainted with the particnlars of this 
erent, J can assnre 70a that this is an equivocation, and a very 
^t mystification. I have had the stone in my hand, and there 
» not the least appearance of the classical crust or varnish of 
lerolites, nor of the composition of the meteoric stones I have 
nen and so attentively examined at the British Museum and at 
tlie Jsrdin des Plantes. 

It is not difficult to understand from the circumstances 
attending the &11 how this equivocation has originated. It was 
a?ery stormy evening, and an electrical explosion took place, 
which traversed a gallery in the house of the parish priest. A 
nil was pointed out against which the flame of the alleged 
leroltte struck. At the same time some noise of a &A\en body 
VM heard, and a stone not previously existing in that court was 
hmd ; hence the conclusion that a meteor had fallen at Supino. 
A German assistant to a Professor at the University went im- 
■Bdiately to Supino and gave fifty francs for a piece of the 
(ione. The owner of the house thought that he had really re- 
ooTed /rom the heavejia a treasure to provide the means for a 
<ioiation to a nephew on his approaching marriage, and, as this 
WIS near, he asked fabulous sums for the remainder of the stone. 
^ni. De Rossi visited the place and was persuaded that the 
galleiy could not have been traversed by the stone, but only by 
the lightning. No hole of any depth was found in the place where 
^ stone fell. He brought it to Rome ; and when I saw it we 
Were convinced that it was only a piece of volcanic pumice, 
which is frequently found in that district, an extinct volcano 
dicing at no great distance. 

The fall may be explained thus. In this country it is 
<^Q8tomary to place stones on tbe tiled roofs of the houses, to 
Prevent the tiles from being blown away by the winds. A 
▼olcanic stone was probably on the roof, and the lightning struck 
H^unst it as a more conducting material, and threw it into the 
^rt. This explanation, which is very simple, is very probable ; 
»ie noise heard was not that of a meteor, but that of the thunder 
storm. 

I have considered it my duty to inform the Society of the 
*We facts, to avoid mystification. 

^OTiie, April 19, 1877. 



112 



366 Mr, J, W. L, Olaisher, Chi an EUiptie xxxm. 7» 



On an Elliptic Function Solution of Kepler^s Problem. 
By J. W. L. Glaisher, M.A., F.R.S. 

§ I. In a paper recently published by the German Astrono- 
mical Society,* Dr. Hugo G^ld^n has applied the Theory of 
Elliptic Functions to the solution of Kepler's Problem in the 
following manner : — 

Writing the equations in the form 

^°^^-y(i3-:)t"iE (') 

M = E-tf8inE (2)t 

(where M, = n^+^^i is the mean anomaly, E the eccentric ano- 
maly, and / the true anomaly) Dr. Gyld^n takes ^E equal U^ 
the amplitude of an elliptic integral — viz. he puts 

— E = am w, 

2 

the modulus k being given by the equation 

SO that A;' = y^/l^ZlY and thus the equations (i) and (2) 
become, on writing ^f = am u, 

coam It = 90*^ — am» (4) 

M ~ 2amv— « sin (2amt;) (5) 

The quantities r, x, y are also readily expressible in terms of 
elliptic functions of u or v. 

The equation (5) may be written 

M = 2anit; — 2«snvcn t> 

= 2ami; + |^— ,(amt;) (6) 

and from the Theory of Elliptic Functions we know that 

2amt; = 2t? + -^^ sin 2t| + - -^^-7 sin 4TI + &C. . . (7) 

I +J* 2 1+2* 

* "Zur Auflosung des Kepler'schen Problcmes.'* Vierteljahrsachrift der 
Astronomitchen GeseUschqft, t. x. (1875), PP* 285-296. 

t I have slightly altered the notation : Dr. Gylden writes (2), y = c — e sin c. 



May 1^77. Function Solution of Kepler's Problem. 367 

i| being written in place of -^r^v, so that, taking account of the 
irelne of e giTen by (3), the eqaation (6) becomes 

- &c (8) 

This eqaation is used to replace (2), viz. — given e we can 

calculate k from (3), then q from jb, by known elliptic function 

2K 
fonnule, and log — from q, by means of the eqaation 

S3 (l+2j + 29^ + 2j*+&C.)*. 

IF 

We tbns obtain the nnmerical values of the coefficients of sin 2 17, 
im 417, &c., in (8), and can determine by successive approximation 
the Talue of 2 17, corresponding to a given value of M, and thence 
from (7), the value of 2 am v, that is, of E. 

§ 2. Thus, in this method, the expression (2) is replaced by 
^two formulsB (7) and (8), which, though more complicated, 
^ such that the convergence of the successive approximations 
w more rapid ; in fact, the simplicity and slow convergence of 
(2) are exchanged for the greater complication and quicker 
convergence of (7) and (8). Of course, the question of whether 
^<^e exchange is an advantageous one can only be definitively 
■cttled by careful numerical comparisons. 

In what follows I propose to discuss the general nature of 
snch an elliptic function solution of the problem as Dr. Gyld6n 
proposes, and to examine, in particular, what value should be 
•"signed to the modulus in order that the convergence of the 
I^Pproziinations may be rendered as rapid as possible. It will 
^ sbown also that the calculation of the coefficients in (7) and 
(B) may be much facilitated ; and some remarks upon the ques- 
tion of the practical utility of the method will be found in § 13. 

§ 3. It is readily seen that the solution of the equation 

X ^ a + n<l> (j), 

^*iepe n is small, by successive approximation is equivalent to 
®*panding x in powers of n by Lagrange's theorem, viz. : — 



368 Mr, J. W. L, OlaisheVf On an Ellipiie xxxyii. 7, 

Firtt approximation x =s a; 
Second „ x » a + n^ ; 

Thiid „ X wma-^n^^a + n^) 

Foorth „ X m a + n^{a + nfa -1- 91*^^'^) 

« fl + n^ + n^^a^'a + n«^ (^'rt)* + ^ n^i^paf ^"a + &c. 

^^ 1.2 lia^^^' 1.2.3 rfa*^' 

go ihat the rtb approximation differs from the truth by a quantity 
of the order n^ ; and by the diminution of n the rapidity of the 
convergence of the approximation is very considerably increased. 

The object in view is thus to render the coefficients of 
sin 217, sin 417, sin 617, &c., as small as possible, without unduly 
increasing the number of terms that must be included. 

Besuming the equations (6) and (7), we have 

2amv " 21?+ ^, Bii/2i? + - y. sin 4i} + &c. 
I +2* 2 I +9^ 

— I snvcnty ^ . sin 2ij + 2-^-^ Bin 417 + &c. 
» / 1+2* i+j* 

80 that, writing for brevity 
we have 

M « 2aint;~2f8nvcnt; 

4.(7 
-»2i?— ( E^— I) --^sm 21J 

-&c (9) 

or, as we may write it^ 

M = 21?— (A,e- B,) sin 21? 
— (A,f— B,) sin 41? 
~(A,e~B,) sin 61} 
- &c (10) 



where 






/ 



fiaj 1877. Function Solution of Kepler* s Problem, 369 

For T&laefl of the modular angle that are not veiy consider- 
able q is Teiy small, and therefore B| is small, and as we know 
that the series 

A| sin 21} + A, BID 41} + A, sin 611 + &e, 

IS the sine of the series 

21} + Bi sin 2i| + B, sin 41} + &c., 

it is dear that, for yalnes of the modular anffle that are not near 
90^, Ai will not differ much from unity ; but tiae following numbers 
show at a glance the variation of A| and q as the modular angle 



mcreases. 






k 


A. 


9 


sin 15^ 


099991 


000433 


sin 30® 


, 099839 


0*01797 


sin 45^ 


0*99071 


0*04321 


sin 60'' 


0-96399 


008580 


8in75<» 


087701 


0*16303 



Thus, for values of the modular angle less than 45^, the value 
of Ai does not differ from unity by the one-hundredth part, 

and the value of q is less than — Speaking roughly, the values 

of A« and B„ are respectively equal to q A«., and q B,..], so that 
for all values less than 60° the series (9) is very convergent, 
while Ai differs very little from unity. The method would 
evidently not be a suitable one if the angle were as large as 75^, 
and in what follows the angle is supposed not to exceed 50° or 
6o^ 

§ 4. The coefficient of sin 2 ?; in (10) can be made to vanish if 
the modulus A; be so chosen that Aj c = B^ ; that is, taking A^ := i, 
if approximately 



« = 7^ =4} nearly; 



or 



I 

o = - c. 
^ 4 



In order to obtain exactly the order of the first term when 
q has this value, it is necessary to use the expression for I — I 

in terms of q, viz. 

V IT / i—q' i-q* I— }*• 



4? (i +42* + 6j* + &c.); 



37© -MV-* «^- ^- ^- Qloisher, On an Elliptic XXXTII. 7, 

whence, rejecting powers of q above cabes, 



R=» 



_ '-4g' . 



42(1+42*) 42 
so that, when e = 43, 

R<j « 1—42' 
and the coefficient of sin 2 rj 

"^^VTT7"i+2*/ 

and thus, retaining only the terms of the highest order in e in 
each coefiBcient, the equation (10) becomes 



M 



21? + - e' sin 21J— f 2 — j- «* sin 4'? — (s— ~)-^ ^ sin 6if 

— (4 — j — e* sin 81?— &c. 

= 2i» + - «• sin 21? — 4«' sin 41J— ^^^ sin 6ij— — ^e* sin 8i|— &c. ; 
4 00 250 

SO that M differs from 2 17 only by quantities of the order e*. 

The value of 5 for which the coefficient of sin 217 exactly 
vanishes is, as is evident at sight from (9), given by tlie equa- 
tion 



that is, by 



giving 






« = 42+ i6q* + g6^-¥&c. 



1 I , 21 

2 = - f — Z^ + 7" 
^ 4 16 51 



- c* — &c. 

2 



and therefore 2 = e is a very close approximation. 

§ 5. The special point of advantage that the elliptic function 
solution offers is now apparent, viz. in the equation M =: E — e sin E 
we replace E and sin E by two series, the former being of 
the form 2?/ + B,Bin 2?; + B2 8in 4?/ + &c., and the latter of the 
form Ajsin 2i;4-A2sin 4>; + &c., but we have at our disposal a 
certain quantity (the modulus) on which the values of Ai, 
Aj . . . Bi, B2 . . . depend, and we can so select it that the co- 
efficient of sin 2?; in the combined expression for M may be 
very small, and aIso the coefficients of the succeeding terms. 



May 1877. FuncHan Solution of Kepler* a Problem. 371 

In his solution Dr. Gyld^n has not chosen his modnlns with 
ibis yiew, bnt, as mentioned in § i, he takes 

ibis yalae being assigned to Je, not in order that the coefficients 
in (10) may be rendered as small as possible, bnt that the 
equation (i), viz. — 

DU17, ^y comparison with the elliptiQ function relation 

^ tan am u = , 

tan coamu 

be converted into the relation 

coamu » 90^— amv. 

^08 the object in view in determining the modulus was to obtain 

^ analytical transformation of the problem of two bodies ; but 

tf the solution of Kepler's problem be alone considered — and to 

^ Dr. (3yld^n restricts himself in the numerical examples that 

be gives in his paper — there seems no reason why the modulus 

■bonld not be selected so as to render as rapid as possible the 

Approximations. If we calculate E directly from the equation 

« = E— e sin E we have the case corresponding to A; =: o : here 

tbere is only one term to be calculated at each approximation, 

but it is large, viz. of the order e. When, instead, we replace E 

^ sin E by series, we have more terms to calculate at each 

H^proximation, but then we can so determine k that the largest 

Wm may be of the order 6*. If the value of k so obtained (that 

IS fronx the equation 4^ = e) gave so large a value of q that very 

iQany terms had to be included, it would be necessary to consider 

whether it would not be desirable to give some smaller value to 

9« even though the magnitude of the largest coefficient would 

^tta be increased. It will be found, however, that for all the 

^Hlaes of e for which the method is suitable, the value of q is 

^efficiently small to render the convergence of the terms rapid, 

^^ that the assumption 4q = e need not be modified on this 

^^^unt. 

§ 6. As the equation 4^ = e is only obtained as an approxi- 

don to the equation Ai6:=Bi, it is clear that there is no 

'antage in its being exactly satisfied, and it will generally be 

^^ply sufficient if the modular angle be taken equal to the exact 

^^jiher of degrees nearest to the angle for which 49 = 6. 

The following Table gives the values of the coefficients 



i 



372 



Mr. J. W. L. OlaUher^ On an EUipiic XXXYIL 7, 



and also the Talues of q and logq for every degree of the 
modular angle. The valnes for angles at all near 90 would noi, 
of coarse, be used, but it seems desirable to give the Table in its 
integrity. 







ThbUI. 






Ajcnnk 


A. 


B. 


9 


logq 



I 


1*0000000 


0-0000762 


0*00001904 


5-27965680 


2 


I -0000000 


0*0003047 


0-00007617 


5-88178296 


3 


0-9999998 


0-0006857 


0*00017143 


623407579 


4 


0-9999995 


0-0012 1 95 


0*00030487 


6*48410778 


5 


09999989 


0*0019063 


000047657 


6-67812662 


6 


0-9999976 


0*0027466 


000068665 


6*83673234 


7 


09999954 


0-0037409 


000093522 


697091369 


8 


09999924 


0*0048898 


0*00122245 


7*08723006 


9 


0*9999882 


0*0061940 


0*00154850 


718991248 


10 


09999817 


0-0076543 


0-00191359 


728184993 


II 


09999730 


00092717 


0*00231795 


736510313 


12 


0*9999619 


0*0110472 


0*00276181 


7 441 19369 


13 


09999476 


0*0129817 


0*00324547 


7*51127726 


14 


0-9999289 


00150767 


0*00376923 


7*57625221 


15 


0-9999059 


00173334 


000433342 


763683083 


16 


09998783 


00197532 


0*00493841 


769358743 


17 


09998441 


0-0223377 


000558460 


774699184 


18 


09998034 


00250886 


oxx)627239 


779743338 


19 


09997550 


00280077 


000700226 


784523825 


20 


09996982 


0-0310968 


000777468 


789068255 


21 


09996311 


0-0343582 


000859018 


7*93400202 


22 


09995537 


00377938 


000944930 


797539964 


23 


0:9994644 


00414061 


001035265 


8 01 505 1 37 


24 


0-9993617 


00451976 


0*01130084 


8-0531 1085 


25 


09992446 


00491708 


001229456 


80897 1 301 


26 


0-9991 1 15 


00533285 


00133345 1 


8- 1 2497701 


27 


09989607 


00576738 


001442144 


8-15900867 


28 


09987908 


00622096 


001555616 


8-19190236 


29 


0*9986000 


00669393 


001 67395 1 


8-22374268 


30 


0-9983865 


0*0718663 


0-01797239 


825460576 


31 


0-9981482 


00769944 


0-01925575 


8*28456038 


32 


09978827 


00823275 


002059060 


8-31366893 


33 


09975884 


0-0878696 


0-02197800 


8*34198819 


34 


09972621 


00936250 


002341909 


836957004 


35 


0-9969019 


00995984 


002491506 


8*39646198 



Haj 1877. Function SduHon ofK^ler^a Problem, 



373 



3^ 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

56 

57 
58 

59 
60 
61 
62 

63 

<^ 

^S 
66 

^7 
68 

To 

7i 
7^ 

>3 
^^ 



A. 
0*9965046 
0-9960677 

0-9955875 
0-9950616 

09944852 

09938557 
0*9931682 

09924188 

0*9916026 

0*9907150 
09897501 
0*9887027 
09875664 
0*9863346 
0*9850005 

09835562 
0-9819934 
0*9803034 
0.9784766 
0*9765026 

0-9743697 
09720666 

09695790 
0*9668930 
0*9639930 
0*9608609 
09574782 

0-9538241 
09498751 
0*9456061 
0*9409892 
09359923 
09305806 
0*9247144 
0*9183501 
0-9114365 
0-9039167 
08957248 
0*8867853 
0*8770097 



B. 
0*1057946 
O-II22187 
0-1188761 
0*1257725 
0*1329139 
0*1403068 

01479578 
0-1558741 
0*1640633 

01725335 
0*1812931 

0-19035 1 1 

0-1997 1 72 

0*2094017 

0-2194155 

0-2297702 

0*2404780 

0-2515525 

0*2630077 

0*2748590 

0-2871227 

0*2998163 

0-3129590 

0*3265712 

03406752 

03552952 

0-3704574 
0*3861905 

04025257 

0*4194977 

0-4371446 
0*4555081 
0*4746350 

04945775 
05153942 

0-5371509 
05599223 

05837942 
0*6088652 
0*6352492 



0*02646718 
002807680 
0-02974532 
0*03147428 
0-03326526 
00351 1996 
0-03704020 
0-03902789 
0-04108507 
0-04321392 
0*04541675 
0*04769603 
0-05005441 
0*05249471 
0*05501993 
005763334 
0*06033839 
006313883 
0-06603869 
0*06904230 
007215437 

0-07537997 
007872464 

008219438 

008579573 

008953588 

009342267 

0-09746475 

0*10167168 

0*10605402 

0*11062354 

o" 539337 
0*12037825 

0-12559479 

0-13106182 

0*13680085 

0*14283652 

0-14919737 
0*15591666 

0-16303353 



8*42270772 
8*44834754 
8*47341870 

849795576 
8-52199088 

854555404 
8.56867332 

8*59137506 

8-61368404 

8*63562365 

8*65721604 

867848227 

8*69944237 

8-7201 1550 

8-74052006 

8-76067376 

878059371 
8-80029653 

8*81979842 

8-83911525 

8*85826262 

8-87725598 
8*89611069 

8*91484211 

8-93346569 
8*95199709 

8*97045226 

898884758 

9*00719999 

9-02552714 

904384755 
9*06218085 

9-08054801 

9*09897161 

9*11747621 

9-13608879 

9* 1 5483926 

9*17376116 

9*19289252 

9*21227694 



374 


Mr, J. T 


r. L. Gladsher, i 


Dn an EUipHe 


XXIYIL 7, 


Arosinl 


A. 


B. 


9 


log9 


ll 


0-8662938 


0-6630809 


0*17059454 


9*23196512 


77 


08545150 


0*6925190 


0*17865566 


9-25201679 


78 


08415247 


0*7237544 


0*18728518 


9*27250342 


79 


0*8271432 


07570202 


0*19656766 


929351207 


80 


0*8111467 


0*7926045 


0*20660976 


9*3i5>5o82 


81 


07932526 


0*8308727 


0*21754895 


933755699 


82 


07730953 


0*8722976 


0*22956716 


9-36090976 


83 


07501866 


0*9175126 


0-24291297 


9*38545071 


84 


07238497 


0*9673968 


0-25794020 


9 41 I 5 1903 


85 


06930978 


10232358 


0-27517980 


9*43961656 


86 


0-6563906 


1-087040 


029548839 


9-47054042 


87 


0-6110736 


1*162285 


032040034 


9*50569296 


88 


0-5517805 


1*256006 


o-353'6565 


954797845 


89 


0-4637601 


1-387542 


0*40330931 


960563824 



By means of this Table we can always, for any given yalne 

of e (supposed less than ^) at once select that value of the 

modnlar angle for which the valne of Aje— B| is the least. In 
the formation of this Table, eight-decimal valaes of log q and 
log K were nsed, and log A| and log Bi are given to eight places 
(except above 85°) in Table II., at the end of the paper. The 
values of A^ and B^ were deduced from, those of log A| and 
log B] in Table 11. by means of ordinary seven-figure logarithms, 
so that the last figures are not to be relied upon ; this applies of 
course especially to the numbers in the A] column, which, com- 
mencing generally with nines, were taken out from near the end 
of the table of logarithms. The values of q, however, were ob- 
tained by ten-figure logarithms, and should be correct to the last 
figure. 

§ 7. I take as an example the case of e = -, M = 50^, which ifi 

4 
the first of the two examples which Dr. Gylden has given in his 

paper. We see at once fix)m the foregoing Table that Bj is most 

nearly equal to -Ai when Aj = sin 52° ; and taking this value oi 

4 
the modulus and working with seven-figure logarithms, I find 



A, = 0-9819934 
A2 = 01 1 89336 
A, = 00107645 
A4 = 00008660 
Aj = 00000653 
Ag » 0-0000047 
A 7 - 0-0000003 



B,= 
B,= 
B,= 



o- 2404780 
00072813 
0-0002929 
0-0000133 
0-0000006 



Mfty 1877. J^^unction Solution ofKepler^s Problem. 375 

I 



wbenoe, e being = -, 

4 



2 1} B M + 0*0050203 sin 2 1| 
4-0*0224521 sin 41} 
+ 0*0023982 sin 61} 
+ 0*0002032 sin 81} 
+ 00000157 sin ioi| 
+ 0*0000012 sin 1297 
+ 0*0000001 sin 141} 
+ &C. 
and the formulaa are 



2i| = M + [3*01515] 


sin 297 


E*2ij + [4*6955006] 


sin 21} 


+ [3-665682] 


i sin 411 


+ [3*176637] 


sin 41} 


+ [26943] 


sin 61} 


+ [1*7811] 


sin 61} 


+ [1*6223] 


sin 81} 


•*- [0437] 


sin 8i| 


+ [0*510] 


sin 101} 


+ [9*120] 


sin lori 


+ [9394] 


sin 121} 


+ &C. 




•*-[8-3i] 


sin 1411 






+ &C. 




• 


. . (I 



where the numbers in [ ] denote the Briggian logarithms of the 
coefficients expressed in seconds of arc. 

When M is pnt = 50° the successive approximations to 2 1| 
are found to be 



// 



50 

51 33 4 

51 31 51-4 

51 31 524 
51 31 524 

whence, from the formula for 2 am v, z= E, it results that 

E = 62<> 43' 55"*9. 

§8. In Dr. Gyld6n's paper the process is as follows : — 

e = -, whence *« = , A^* = -, 
4 5 5 

^'^d using the formula q = \ + 2X*+&c. 
^here 



^^ ia shown that 



2 il + k^(l+^/k'y' 



logq^ 8*503565 ; 



ice, from the formula 

2K 

log ^- == 0053694. 

It is thus found that 

211 « M+ [4398392] sin 2i| 2ani« - 2if-f [4*419607] sin 3i| 

■f [3*455685] sin 411 + [2-62258] sin 411 

+ [216940] sin 6if +[0*950] sin 6 If 

+ [0799] sin 8n + [9 319] ■>» S'l 

+ [9-415] sin loif +&C. 

+ &C. . . . (12) 

Dr. Gyld^n starts with 2 1| = 56^^ as a first approximation, an 
finds the successive approximations to be 

56 32 4 
56 32 62 

giving 

E, = 2am», = 62^ 43' 56''o. 

But in order to compare the approximations by means of (12) 
with that obtained from (11), it is necessary to commence the 
approximation with 2 1| = 50°. The approximations thus obtained 
are shown below in the second column ; and for the sake of com- 
parison those derived by the direct defcermination of E from the 
equation 

E = M + -sinE. 
4 
that is from 

E -M + [47i2365i] sinE (13) 

arc added in the third column. 

« « - , M c= 50^. 



Vpproxim«iions 


A i^nix i {nations 
obtAinft.1 from (13). 


Approximations 
obtained from (13) 


e 


1 


It 





1 


u 





$ 


u 


5<^ 






50 






50 






5« 


.v^ 


4 


56 


7 


35 


60 


58 


22 


>« 


.>« 


5«4 


56 


30 


46 


62 


31 


29 


Ui 


3« 


5.^4 


56 


3^5 


2 


62 


42 


30 


In» 


3« 


5-4 


56 


32 


61 


62 


43 


46 




pivii 


5? 


t56 


32 


6-3 


62 


43 


54-8 


K - <o 


43 


55 ^> 


.56 


3^ 


^3 


62 


43 


558 








; 


rivin 


*> 

^ 


(62 

4 


43 


55 9 








E - 02 


43 


560 


I62 


43 


559 



May 1877. Ftmction Solution of Kepler^ a Problem, 377 

Thns, not connting the first approximation, viz. 50°, we obtain 
the final value from ( 1 1 ) in three approximations, from ( 1 2) in five, 
and from (13) in seven. The difference of a tenth of a second 
in the values of E is unimportant, as a last-figure error of a unit 
is of course quite possible. It was not necessary to calculate the 
earlier approximations to seconds, bnt it was convenient for the 
sake of uniformity to carry all the approximations to this extent. 

§9. Dr. Gylden's value o£k is %/ (-) corresponding to a 

modular angle of 39° 14', while the modular angle in (11) was 
52*^. The corresponding values of q are 0*03 18834 and 0*0603384 : 
bat only one more term is required in (11) than in (12). 

On calculating the coefficient of sin 217 with Dr. Gylden's 
value of q, I find it to be 

0994935 «-o' 127404 

which, patting e = , becomes 

4 

0248734 — o- 1 27404 

80 that in this case the subtraction of the second series only 
^minishes the coefficient of sin 217 in the first by about one- half : 
And the whole coefficient is equal to about one-half of e. 

Expressed in seconds the values of the coefficients of the 
terms in (11) and (12) are 





In (11). 


In (12). 




// 


// 


Sin 27) 


10355 


250260 


Sin 41} 


4631- 1 


28555 


Sin 677 


4947 


1477 


Sin 8tj 


419 


63 


Sin 1077 


32 


03 


Sin 1277 


02 





and the sum of all the coefficients in (11) is 6207" or 1° 43' 27'', 
and in (12) 28036" or 7^47' 16". The coefficient in (13) is 
51566'' or 14^ 19' 26". 

Another advantage that results from obtaining the modular 
angle from the Table in § 6, instead of determining it as an 
analytical function of e, is that in the former case all the 
necessary tables can be calculated beforehand. It was this, in 
fact, which, when reading Dr. Gylden's paper, first led mo to 
examine the subject, as the existence of an exact analytical re- 
lation between q and e required that the computer should him- 
self calculate, for each given value of c, the values of K and q ; 
and this would be avoided if use could be made, instead, of a 
small table of these quantities. In the practical applicatioir of 
the method, it certainly would be an important gain, both in 



s 



Function Solution of Kepler* 8 Problem. 379 

^ far as possible, the numerical calcalations re- 

^^n of Kepler's problem. I have confined 

^^lation of Kepler's problem — ^that is, to 

^frpm the equation E = M+c sin E by 

>r~aud though it is tme that Dr. 

'^examples in his paper, he does not 

b^ considered the solution of this question 

.deral investigation. If the true anomalj 

>i of M, probably the best method would in 

^ .iain E from M and then to deduce/ from E by 

^1 formula (i). 

.dla for tau ami; is 

-j^ {tan 7,--''^., sin 21, + - J^^ sin 4i?-&c.}, 

is clear that since the (/-coefficients are different from 
in the series for ami; or snv cnv, it would be most con- 
t to first calculate E, = 2 amv, and then have recourse to 
obtain/. Also the form into which (i) is transformed, 
ami* = 90"— amr, that is, am (K— «) ^ 90°— amv, or, as 
Y write it, 

K-tt = r(90^-^E, ^0, 

preferable to (i) for the calculation of tt or/; so that, as 
^he numerical solution of Kepler's problem is concerned, 
Ine of k given by (3) does not present any special ad- 
es. 

2. The other example which Dr. Gyld^n takes is ^ = '» 

0^ It is not a very satisfactory one for the method in any 
8 is rather too large ; and it is even less favourable as 
mple of the process of solution suggested in this paper, for 
reasoning in §§ 4 and 5 e^ has been supposed to be cou- 
)ly less than e, and this is not the case if e be as large 



this case the Table in 


§ 6 shows that Ai e — Bi is 


i smallest 


k = sin 68% and the f ormulce are 






M- [3-28499] 


sin 2ri 


2am t; « 


= 2i» + [49907850] 


sin 21} 


+ [4-242028' 


sin 41} 




+ [3*77646] 


sin 41} 


+ [3*57437] 


sin 61} 




+ [2-68101] 


sin 61} 


+ [28035] 


Bin 8i| 




+ [16366] 


sin 8f| 


+ [1-9915] 


sin lori 




+ [0-620] 


sin ion 


+ [1-1568] 


sin 121} 




+ [9622] 


sin 121} 


+ [0-308] 


sin 141} 




+ [864] 


sin 141} 


+ [9*455] 


sin 1617 




+ &C. 




+ [8*59] 


sin 181} 








+ &e. 






• . 


. rid) 



F F 



378 



Mr. J, W. Xr. Glcusher^ On an EUipUe xxxm. 7, 



point of labour and accnracj, to bave the K's and g's given, as 
the necessity for the calcnlation of them by the nser of the method 
seemed of itself to form a serious objection to its employment, 
except in those cases where so many valnes of E were reqnuned 
that the preliminary calculations might be relatively disregarded. 

§ 10. By means of the equation qs=- ewe can of course ex« 

4 
press k in terms of 0, though the general term cannot be exhibited^ 

as there is no g-series for k. Starting, however, with the seri* 

for log kj vis. : 

^ ^-^ 3f ,^.^ 2(1+9*) 3{i+f) 



we have 



log 4^9-4^+69'-— j* + 39*-&c. 



= 4v/9{i-49+i4j*— 409»+ioi9^— &c} 



Dr. Gylden's value being 



?^-S. 



= ^/(20{l--« + §«*-^^ + &C.). 

Thus the former series gives the greater value of q ; but the 
following table shows better the amount of difference between 
the formuke : 







(«)? 


I 
4 


w* 


V( 


I +«/ 




e 


k from 


(«> 


k from (/3) 


e 


k from (a) 


X: from (/3) 


m 


e 




• ' 


f 







# 


I 
20 


25 




17 59 


-i 
20 




52 


39 14 


2 
20 


35 




25 14 


6^ 
20 




56 


42 48 


3 
20 


42 




30 43 


.7_ 
20 




60 


46 4 


4. 

20 


4S 




35 »6 


8 
20 




63 


49 6 



§ 1 1. Dr. Gjlden seems, as stated in § 5, to have been led to 
the value of the modulus which he lidopted by analytical con- 
siderations, which have reference to the treatment of the general 
question of elliptic motion ; while in this paper the object has 



May 1877. Function Solution of Kepler' a Problem. 



379 



been to reduce, as £ar as possible, the numerical calculations re- 
quired for the solution of Kepler's problem. I have confined 
myself entirely to the solution of Kepler's problem — ^that is, to 
the determination of E from the equation E = M+e sin E by 
means of elliptic functions — and though it is true that Dr. 
Oyld^n does so too in the examples in his paper, he does not 
appear to have specially considered the solution of this question 
9i^ri from the more general investigation. If the true anomaly 
/be required in terms of M, probably the best method would in 
every case be to obtain E from M and then to deduce/ irom E by 
the trigonometrical formula (i). 
The g^-formula for tan amv is 



2>fc'K 



{tan ij — ^^. sin 2ij + -^^ sin 41J— &c.l, 



5- 1+2^ 

and it is clear that since the (jr.coefficients are different from 
these in the series for amv or snv cnv, it would be most con- 
venient to first calculate E, = 2 amv, and then have recourse to 
C O to obtain/. Also the form into which (i) is transformed, 
viz. coamt^ = 90°— amt', that is, am (K^u) = 90°— amv, or, as 
'^o naay write it, 

K-f* = F(90^-^E, i-), 

18 not preferable to (i) for the calculation of u or/; so that, as 
far Its the numerical solution of Kepler's problem is concerned, 
toe value of k given by (3) does not present any special ad- 
vantages. 

§ 12. The other example which Dr. Gylden takes is e = ~, 
_ 2 

M ^= 60®. It is not a very satisfactory one for the method in any 
^^^se, as 6 is rather too large ; and it is even less favourable as 
wi example of the process of solution suggested in this paper, for 
^ the reasoning in §§ 4 and 5 e' has been supposed to be con- 
siderably less than e, and this is not the case if e be as large 

In this case the Table in § 6 shows that Aje — Bj is smallest 
^neu ]c = Bin 68°, and the f ormulie are 



^v =* M- [3*28499] 8 
+ [4-242028] s 

+ [3*57437] 8 
+ [2-8035] 

+ [1-9915] 
+ [1-1568] 

+ [0308] 

+ [9-455] 
+ [8-59] 
+ &«• 



n 21} 
n 41J 
n 6ri 
n 811 
n lori 
n I2fi 
n 141} 
n 1617 
n 181} 



2&mv Si 2fi^ [49907850] 8 

•*• [377646] 
+ [2'68ioi] 

+ [16366] 

+ [0-620] 

+ [9-622] 

+ [8-64] 

+ &C. 



n 21} 
n 41} 
n 61} 

n 89 
n ioi| 
n 121} 
n 141} 



(14) 



¥1 



380 Mr. J. W. L. Olaisher, On an Elliptic xxxvii. 7, 

Dr. Qyld^n has 

and his fbrmnlffi are 



211 -M+ [4-650549] 


sin 2if 


+ [4-075356] 


sin 4if 


+ [3-12280] 


sin 617 


+ [2-0940] 


sin 817 


+ [1*029] 


sin lOfi 


+ [9-945] 


sin 1217 


+ [8-86] 


sin 1417 


+ &C. 





2am t; 



2 1»+ [4-748494] sin 


21J 


+ [3*283498] sin 


4'? 


+ [1-9415] sin 


6u 


+ [0-651] sin 


8u 


+ [9-387] sin 


101} 


+ &C. 





. . . (15) 

while the original eqnaiion E = M+6 sin E becomes 

E=xM+ [5-0133951] sin E (16) 

The approximations derived from these three formnlie are 
shown below : — 









• 
2 


, M = 6o°, 




From (14). 


Fi*oin (15). 


From (16). 




60 


/ 






60 


/ 


// 


/ // 
60 


63 


34 




73 


36 




84 49 


63 





26 


73 


26 


15 


88 32 


63 


5 


48-6 


73 


26 


39*4 


88 38 19 


63 


4 


57*2 


73 


26 


383 


88 38 233 
,88 38 233 


63 


5 


5*5 


73 
73 


26 


384 


63 


5 


41 


26 


38-4* 




63 
I63 


5 


43 




giving 




5 


4*3 


E«88 


38 


232 






giving 










E-88 


38 


23*4 











Thus, nsiDg (14) there are seven approximations, using (15) five, 
and nsing (16) only four. The reason of this is that tbo 
greatest term in (15) is the first, viz. that which involves sin 2 77, 
and as 2?; in this example is equal to about 73°, a small change 
in the angle produces but a slight alteration in the sine, and the 
approximation is rapid. It is even more so in (16), where the 

* I have recalculated and slightly altered Dr. Gulden's last approximations, 
so that all three sets should be exactly similar to one another. Br. Gyld^n's last 
two approximations are 73<> 26' 39"*4 and 73® 26' 38"-2, giving E ■» 88® 38' 23"o. 



Maj 1877. Fundiofi Soluiioth 0/ Kepler's Prohlem. 



381 



angle is yeiy nearly equal to 90^. Bnt in (14) the greatest 
term is that which inyolves sin 411, and 417 is eqnal to about 
126% Trhich is not far distant from the middle of the quadrant, 
so that a change in 2 1| produces a considerable alteration in the 
▼ahie of sin 417. All this will be reversed when 417 in (14) is 
nearer to 90^ than 211 in (16). Take for example M = 30*^ and 
the approximations are as follows : — 



e 



:si = 300. 



From (x4}* 
# // 


From ds). 
/ // 


From (16). 

/ M 


30 


30 






30 






35 8 


39 


2S 




44 


19 




35 22 25 


41 


28 


32 


50 


I 




35 22 440 


41 


49 


5 


51 


57 


3 


35 22 443 


41 


52 


24-6 


52 


33 


35 


35 22 443 


41 


52 


56-6 


52 


44 


46 


giving 


41 


53 


1-8 


52 


48 


9 


.52 49 37-6 


41 


53 


2*6 


52 


49 


II 




(41 


53 


2-8 


52 


49 


29 




I41 


53 


2-8 


52 


49 


34*9 




1 


giving 


52 


49 


367 




£ = 52 


49 


37-6 


52 
52 

52 


49 
49 
49 


37*2 
37*4 
375 










49 


375 



Here 4 >; in (14) is equal to about 71**, and 217 in (15) to about 
42® ; and as E is only about 53° the approximation by (i6) is 
not very rapid — in fact, by (14) there are four approximations, 
by (15) eight, and by (16) thirteen. 

In this case of e = there is not much to choose between the 

2 

two formulae, as the reasoning in § 4 is not appropriate when e is 

so large : for the object was to cause the term of the first order 

in e to nearly disappear, the next term (in which the coefficient 

3 
was approximately = 7; e^) being the largest ; but as this term 

iuTolyes sin 4 77, a small change in the value of 2 77 produces double 
the effect that it would if sin 2 ?; were involved instead ; so that 

when e = - the advantage arising from the term being of the 

second order is nearly neutralised. This is pretty evident ; but it 
mny be seen perhaps more clearly by expanding x by Lagrange's 
theorem (i) when iV = M + e sin aj and (ii) when «= M+e sin 2x, 

F F 2 



382 Mr. /. W. L. Oktlsher, On an EllijpUc xxxyn. 7, 

The yalaes of the coefficienis of the terms 10 (14) and (15) 



are 





In (14). 
u 


In (15). 


sin 2ri 


19275 


44724*9 


sia 417 


17459-3 


11894*8 


8111 61} 


3752-9 


1326*8 


bin 81? 


6361 


124-2 


sin 10 1| 


981 


107 


Bin 121} 


14-3 


0'9 


Bin 14^ 


2*0 


01 


sin 161} 


03 





and the sum of all the coefl&cients in (14) is 23890" or 6° 38' 10", 
and in (15) is 58082" or 16® 8' 2". Only one more term is re- 
quired in (14) than in (15), as the term in sin 1817 can never be 
sensible. The coefficient in (16) is equal to 103132" or 28® 38' 52". 
§ 13. In regard to the practical use of the method Dr. GyldSn 
remarks, and very truly, that the calculations are much less 
laborious than at first sight they appear to be, as only approxi« 
mate values of the arguments are required in the smaller terms. 
Also when 217 is found the value of 2 am t; is obtained with 
great ease, as the values of log sin 2 17, log sin 417, &c., have been 
already calculated. The obvious objection to the method is the 
great number of logarithmic entries that are required : and this 
objection seems so serious as almost to be fatal to its adoption. 
As far as the three examples given in this paper are concerned, 
the old trigonometrical method is certainly preferable ; but this 
might not be the case perhaps if the value of E were smaller, 
say not exceeding 30° or 40°, when the number of approxima- 
tions would be considerable. I must admit that while working 
out the examples in §§7, 8, and 12, the conclusion rather forced 
itself upon me that the method was too complicated and elabo- 
rate for ordinary practical use, and that some of the numerous 
other methods tliat have been given for the solution of Kepler's 
problem must be superior to it. I have, however, made no 
other numerical comparisons besides those described in this 
paper; and Dr. Gylden*s words seem to imply that he has found 
the mode of solution proposed by him to be convenient and 
useful. If a more complete examination should I'ender it pro- 
bable that the elliptic function method might be of practical 
value, I would calculate the necessary tables of the values of the 
second and succeeding terms. My intention was to have ap- 
pended them to this paper, and some of the calculations were 
performed ; but, as the above comparisons tended rather to show 
that the method was not a very good one in practice, they have 
been laid aside: it seems worth while, however, to give the 
values of logAj and logBj for every degree, which are con- 
t^iined in Table II., and the values of the quantities involved in 



May 1877. FimcHon Solution of Kepler's Problem. 383 

the coefficients of the second and third terms, viz., As, Bj, A^, B,, 
for every fifth degree, which are contained in Table III. ; as 
these may be fonnd nscfal in any further discussion of the 
question. Table III. was obtained by means of seven-figure 
logarithms, so that the last figures are liable to small errors. 
Table II. is referred to at the end of §6. I am in gp*eat hopes 
that Dr. (3ylden or some other astronomer who has used the 
method may be tempted by this paper to make some further 
remarlcs in regard to it. 

Whether the elliptic function method should be found to be 
practically important or not, the substitution for E and sin E of 
two series proceeding by multiples of 2 1; and whose coefficients 
depend upon an arHtrary quantity A; is a remarkable trans- 
formation of ihe question, and the form assumed by the equation 
M = E— esin E,viz. 

M = 2 (amt; + "nj^^^ *')» 

is noticeable, for, as a consequence of it, the ^-coefficients of the 
two series are identical, to a factor pres. It certainly seemed 
desirable to examine the efiect of these transformations : and the 
practical advantages and defects of the method could not well 
have been exhibited otherwise than by means of numerical 
examples. ' 

1 ought to mention that Dr. Gjld^n only gives the method 
discussed in this paper as appropriate when e does not exceed 

- : he proposes a different mode of solution by means of elliptic 
functions for the case of 6 > i, which I have not examined. 



TUhUIL 



Aroiinit 


log A, 


log P. 


I 


999999999 


5-88171679 


2 


999999999 


648384295 


3 


999999996 


6-83613578 


4 


999999983 


7-08616777 


5 


999999950 


728018652 


6 


9 99999895 


7-43879211 




999999809 


757297329 


8 


999999676 


7^68928940 


9 


9*99999479 


779197143 





999999202 


788390832 


II 


999998831 


796716078 


12 


9-99993344 


804325038 



384 



Mr. 


. J. W. L, Glaisher, C 


>n an EUipHe xxr 


BSinI' 


log A. 


logB, 



13 


9*99997715 


8-11333269 


14 


999996913 


8-17830603 


IS 


999995919 


8-23888265 


16 


999994702 


8-29563682 


17 


999993226 


834903828 


18 


9-99991458 


839947630 


19 


9-99989354 


8-44727696 


20 


999986877 


8-4927I63I 


21 


999983976 


853602996 


22 


9-99980611 


8-57742085 


23 


9-99976726 


8-61706480 


24 


999972271 


8 655 I I 539 


25 


9-99967176 


869170734 


26 


999961392 


872695978 


27 


999954842 


876097834 


28 


999947456 


879385726 


29 


9*99939161 


8-82568099 


30 


999929872 


8-85652550 


31 


999919498 


8-88645936 


32 


999907951 


8-91554481 


33 


999895137 


8-94383847 


34 


999880934 


8-97139188 


3i 


999865242 


899825244 


36 


999847937 


902446359 


37 


999828889 


905006531 


38 


999807953 


9-07509459 


39 


999784995 


9-09958575 


40 


999759841 


912357055 


41 


999732333 


9-14707871 


42 


9-99702280 


9-17013786 


43 


999669495 


9-19277403 


44 


999633768 


9-21501156 


45 


999594870 


923687340 


46 


9-99552553 


9 258381 13 


47 

• 


9-99506569 


927955541 


48 


999456628 


930041564 


49 


9-99402427 


932098035 


50 


999343640 


934126734 


51 


999279913 


9-36129359 



Maj 1877. Fttndion Solution of Kepler's Problem. 



38s 



ArcHin k 

o 

5« 
Si 
S4 
55 
56 
57 
58 

59 
60 

61 

62 

63 

64 

65 
66 

67 
6g 

69 

70 

71 
72 

73 
74 

75 
76 

77 

78 

79 
80 

81 

82 

83 
84 

85 
86 

87 
88 

89 



log A, 
9*99210856 
9-99136048 
9-99055043 
998967336 

998872383 
998769602 
998658326 

9*98537851 
998407385 

998266051 

9-981 12889 

997946823 

997766654 

9*97571033 

997358459 
9-97127225 

996875396 

996600769 

996300824 

995972642 

9*95612842 

9-95217468 

9-94781856 

994300437 
9*93766522 

9*93171963 

9*92506689 

9-91758073 

990909936 

9*89941153 
988823308 

9*87516937 

985964844 

984079450 

9*8171624 

97860937 

9*7417663 

9*6662934 



logB, 

9-38107544 
9*40062864 
9*41996853 
9*43910996 
9*45806741 
9*47685526 
9*49548740 

951397791 
953234059 
955058935 
9*5^73825 
9-58680151 
960479368 
9*62272967 
9*64062507 
9*6584961 I 

967635984 
9-69423447 

9*71213958 
973009630 
9-74812782 
9-76625982 
9-78452110 
9*80294417 
9-82156648 
9*84043165 
9-85959125 

9-87910753 
9-89905660 

9-91953447 

994066468 

9-96261 199 

9-98560468 

000997574 

00362456 

00653128 

0*0989917 

O' 1422460 



386 


Mr. 


Terry ^ Swne Experiments etc. 


xxxyii. 7, 






TabU ///. 






Arc sin Ir 


A. 


B, 


A. 


B. 


o 

5 


00009531 
0*0038271 
0-0086662 
00155456 


0*0000005 


0*0000007 


0-0000000 


lO 


0*0000073 
0*0000376 


0*00001 10 
0*0000563 
O-OOOI813 


0*0000000 


IS 


O'OOOOOOI 


20 


0*0001209 


0*0000000 


25 


0-0245743 
0-0358984 


0*0003023 
0*0006460 


0*0004532 
0*0009678 


0*0000025 


30 


0*0000077 


35 


0*0497066 


0*0012415 


0*0018577 


00000206 


40 


0-0662368 


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0*0033051 


oxxxx>49i 


45 


00857849 


00037349 


00055607 


oxxx>io76 


50 


O-I087164 


0*0060543 


0*0089724 


0XXX>222I 


55 


0-1354796 


00095335 


0*0140311 


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0*1666215 


0*0147210 


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0*0008420 


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0*2028609 


0*0224921 


00322658 


0-0015904 


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0-2447840 


00343443 


0*0481367 


00030017 


75 


0-2933576 


0*0531223 


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80 


0-3488540 


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TVinUy Collye, Cambridge, 
1877, March 20. 








Some Expeinments Bearing on the Transit of VeiiiirS. 
By the Rev. S. J. Perry. 

A short time since I had the honour of bringing before the 
Boyal Astronomical Society the researches of M. Ch. Andr6 on 
the subject of Instrumental Diffraction in its connection with 
the Transit of Venus, and he has since desired me to supplement 
my paper by one or two historical remarks : — 

1. The main facts adduced by M. Andre were verifications 
of results previously obtained by Schwerd, whose theory was 
completed by Andre. 

2. Professor Kaiser had already pointed out the importance 
of the question of diffraction in the study of telescopic images. 

3. M. Van de Sande Backuysen, successor of Professor Kaiser 
in the direction of the Leyden Observatory, explained the black 
drop as a phenomenon of diffraction in a Note addressed to the 
Astronomische Nachrichten^M&j 11, 1874. 

I have lately received from M. Alfred Angot two very inte- 
resting papers for presentation to the Society. The subject 
matter of these communications is one to which he has, in con* 



Haj 1877. M. Angoiy On ike Phoiographtc Images etc. 387 

junction with M. Andr^, devoted much time and labonr during 
the lart few yean. M. Angot ivas sent as companion to JM. 
Andre, in the French Government Expedition to Noumea, New 
Caledonia, to obeerve the ]ate Transit of Venus, and he has sinco 
been eng^aged in measuring the French daguerreotypes and pho- 
tographs taken on December 8, 1874. I cannot do better than 
let him communicate his results in his own words. 



Etude sur les Images Photographiques ohtenues au foyer des Lunettes 
Astronomiques. Par M. Alfred Angot. 

On sait depuis lougtcraps que I'image photographique d*nn 
objet lumineux est dilatee aux depens des parties obscnres ou du 
champ lui-m^me, et ccia d'aatant plus que I'objet est plus vive- 
ment Claire. Pendant lougtemps, on s'est bom6 k attribuer cet 
effet k un cheminenient do proche en proche de Taction chimique. 
Bans plus r^tudier. Les applications que Ton tente actnellement 
de faire de la photographic aux mesures de precision, notamment 
k celles que demande Tastronomie, rendaient n^cessaire I'^tude 
approfondie de ce ph^nomene. 

Le travail qui suit a ete effectue dans les caves de I'Ecole 
Normale Snpcrieure. Grace a la bienvcillance de M. H. Sainte- 
Claire Deville, j'ai pu mettre k profit toutes les ressources de son 
laboratoire, et m'installer dans nno cavo de 90 metres de 
bngueur en ligne droite, a c6te des appareils qui servaient a la 
mdme ^poque a M. Andre pour son etude do la diffraction dans 
lea instruments d*optique. 

I. March e des E.rpenenc€s, 

Les images photographiques out 6te obtenucs saus grossisse- 
ment au foyer d'une lunette que la Commission du Passage de 
Venus a bien vonlu mettro a ma disposition, et qui m'avait servi 
a Tobservation meme du passage a Noumea (Nouvelle-Caledonie). 
L'objectif, de o™*i3 d'oiiverture, achromatise par Tecartement 
des deux lentilies qui le composent, a 3™'8o do distance focale. 
Une longueur de 1/500® de millimetre, mesurco sur les epreuves 
photographiques, correspond ainsi a un angle de o^'ioq. 

Les epreuves ont ete mesurees avec une des machines con- 
struites par MM. Briinner pour la Commission du Passage de 
V6nu8, et qui permettent d*evaluer rapidement et avec certitude 
le 1/500® do millimetre — quantito bien suffisanto pour mes 
recherches. 

L' objet photograph ie, dispose a environ 87 metres de robjectif, 
est une source luminenso formee do denx rectangles egaux 
separes par un intcrvalle obsenr. Ccs rectangles sont decoupes 
dans une lame metallique que Ton applique sur une plaque de verre 



388 M. Angoiy On the Photogra^kio Images xxxm. 7, 

d^poli, eclairee par derriere avec nne lampe Drammond on. la 
Imniere ^lectrique. On realise amsi un ^olairement nniforme de 
Tobjet pbotographie — condition absolament indispensable. 

Avec cetto disposition on peat obtenir facilement, non-seole- 
ment le ^t de Taugmentation des images, mais la mesore de 
cette augmentation en yalenr absdlnc. L'augmentation de 
dimensions de chaqae rectangle lominenx est en effet forcdment 
6gale a la diminution de rintervalle obscnr compris entre eox : la 
somme de ces deux qnantit^s est done constante et ^gale a ce 
qa*elle serait si Timage se f ormait sealement d'apres les lois de 
Toptiqne geom^triqne. On connidt de plus, par la mesure directe 
de Tobjet photograpbie, le rapport des intervalles obscnr et 
lumineux. Possedant leur somme et leur rapport, on calcnle 
facilement leur valeur pour Timage g^ometrique ; la comparaison 
avec celles que donne la mesure directe des ^preuves donne dans 
cbaque cas, et en valeur absolue, l'augmentation des dimensions 
de Timage. En outre, la Constance de la somme des intervalles 
obscur et lumineux donne un excellent moyen d'appr^cier le 
degre de precision des experiences. 

Pour permettre de juger cette pr^ision, je citerai seulement 
ici les r^sultats suivants des mesures de sept images obtenues 
successivement sur une m^me plaque daguerrienne, et pour 
lesquelles on n'a £%it varier que la dur^ d*exposition a la 
lumiere : 



Largeur (en 1/500" de millimetre) 



da rectangle 
lamineox 

I 

5935 


de I'intervaUc 

obscur 



192-6 


Somme 
786-1 


6i8-5 


168-6 


787-1 


6240 


1636 


787-6 


6326 


155-2 


7878 


6457 


141-4 


7871 


6564 


130-0 


7864 


673-8 


113-4 


787-2 



Dur6c depose 
10 Hocondes 

30 » 

40 .. 

1 minute 

2 minutes 

4 M 

7 .. 

On voit que rcrreur moycniio sur la somme, qui devrait etre 
constante, ne depasse pas o™°*ooi (o'''05). Dans ce qui suit, 
nous nous bomerons a indiquer Texces do Timage sur Timage 
gcometrique calcul^e, comme nous Tavons indiqu6 plus baut, an 

moyen de la somme l-\-Oy et du rapport — mesure directement 
sur I'objet photograpbie, 

II. Resultats, 

Les experiences ont montre que la dimension des images varie, 
lO avec rintcnsit^ de la lumiere ; 2^ avec la duree de pose ; 3® 
avec la sensibilite de la plaque ; 4^ avec le diametre de Tobjectif ; 



May 1877. in the Focua of a Telescope. 389 

5*^ avec I'etat ohimiqae de la plaqne; les phenomcnes etant 
diffi^rents si la plaque a va ou non lo jour avant de rcoevoir rim- 
preHsion photographique. 

I®. Influence de VintensUv. — Touies choscs restant ogales, 
rimage aogmente k meeure que Ton fait croitre rintensite de 
la lamiere; T image obtenue est generalement plus grande que 
rimage geom^trique [en suppoeant un objet lumineux sur fond 
obscnr]. Mais, pour uno intonsitc assez faible, on pcut obtenir 
one image plus petite quo Timage geometrique. Le phenomene 
change de sens si Ton considere Timage d'un objet obscnr sur 
champ lumineux. 

Je citerai seulcment comme ozemple roxporienco suivante, 
qui donne I'exoes de Timago obtenue sur Timago geometrique 
calcnlte pour des intensit^s variant de i a 38 : 

Plaque daguernenne {duree de pose, i minute), 

Bzoii de llmago sur rimogc gtometriquo 



Intenaltddela 
tonroc liunincuz 

I 


en 


1 500^ do mUllmfitre 
1 16' I 


en Hccondes d'arc 
12-66 


1/4 




Sic 


884 


1.9 




41*5 


452 


1/9*5 




392 


4*27 


1/38 




— 22'4 


-2*44 



Le tigne — devant le dernier nombro indique quo rimage obtenue est plus 
pedte que Timage geometrique. 

2®. Influence de la durtie de pose. — La duree de poso a une 
influence de memo ordre quo Tintensite ; Fimage obtenue croit 
avec elle. J*ai cito plus haut un example de eette influence. Le 
resultat general est qu*il n'y a pas proportionnalit45 entre la duree 
de pose et Tintensite, les cffets de la duree de pose etant beaucoup 
moins grands que ceux dc cettc domiere. Un temps de pose i 
avec une intensite 2 produisent, par cxemplo, un effet plus grand 
qu*un temps de pose 2 avec une intensite i . 

3®. Influence de la sensihilito de la plaque, — Pour une memo 
doree de poso ct une memo intensite lumineux les phenomcnes 
s'accroissent avec la scnsibilite de la plaque sans qu'il soit ce- 
pendant possible de donner une loi numerique, la scnsibilite 
n*6tantpas deGnie rigoureusement. Mcs experiences permettent, 
au contrairCy de determiner la scnsibilite en la mesurant, par 
cxemple, par Tin verse de Fintensite luminouse, qui donnora, avec 
une duree de pose de i seconde, une image egale a Timage 
geometrique. 

4®. Influence du dmnudre de Vohjectlf. — Pour verifier la loi de 
Fouverture de Tobjectif, j*ai rednit celui-ci a moitie, mais en 
quadruplant alors Tintensite de la lumiere, de fa9on que I'eclat de 
rimage fut constant, la duree de pose etant alors la memo dans 
les deux cas. 



390 M, Afigot^ On ihe Phoiograpliic Images xxiTiL 7, 

Jc citerai senlcineiit les nombres snivants : 

Excte de rimugo cbtenno nir I'lmage 
g(k)in6triqne en 1/A00<« dc millim^n 
.. , . fouTerturo i 27-0 

Premiere experience • 

^ » 1/2 43*0 

rouverture i 50*2 

Deuxieme experience -L 

r ^ n 1/2 72-0 

L 'image augmente done quand Poavertare de Tobjectif 
diminne. 

5®. Ivfliience de V exposition ani4rieure a la Zfiwiierc— J'ai ex- 
pose k la lnmiere diffuse une moiti^ de chaqne plaque, et j*ai fait 
ensnite sur les deux moiti^s nne serie d'epreuves avee la inline 
dnr^e de pose et la m^me intensity, de fa9on qne tontes les oon- 
ditions f assent identiqnes de part et d'antre, sanf Texposition 
ant^rienre k la Inmidre. L'exp^rience a montr6 constamment 
qne Timage obtenne snr la moiti6 intacte 6tait pins grande qne 
snr celle qui avait prdalablement ct^ impressionn^e par la 
lnmiere diffnse. Je citerai senlement les nombres snivants : 



I** plaque J 
dagnerrienne j 



jintcnsite i 



2® plaque, 
sor collodion -{ 

sec j intensito f 

\^environ 1/4 \ 





Laigenr de I'lmago 


Dar6e do pose 
30 secondes 


dans la partie expoate 
antMenrement H 
la lnmiere 

514-9 


danslapartte 
noncxporte 

5356 


I minute 


537-3 


560-4 


4 minutes 


5630 


581-5 


fi minute 


5845 


6227 


1 2 minutes 


6205 


641-0 


ri minute 


516-5 


558-0 


1 2 minutes 


5585 


5790 



III. Theorle. 



La premiere liypotheso que Ton ait invoquee pour expliqner 
ces faits etait d'admettre nn chemineineiit de proche en procbe de 
Taction chimique. Mais il est facile de voir que telle ne sanrait 
etre la cause de ragraudissement observe generalement, Tont 
d'abord, cette hypothese ne saurait rendre compto de ce fait, 
qn'avec nne faible intensite on une conrte dnree do pose on obtient 
des images plus petites que Timage gcometrique. De plus, s'il 
J avait un cheminement, il devraitetre plus grand sur une plaque 
ayant deja subi Taction de la lumiere diffuse que sur nne autre 
non alteroe, etnous avons vu que T experience donnaitnn resultat 
precise ment contraire. Enfin, en augmentant la duree de poso 
on devrait accroitre le cheminement, en lui donnant pins do 
temps pour se produire, et nne duree depose 2 avcc nneintonsite 
1 donnerait nne image plus grande qu'nne duree de pose 1 avec 



May 1877. i» the Fociis of a Tdescape. 391 

use intensity 2 — ^fiut oontredit par rezperience. II faat dono 
afaandonxier oette hypothdse. 

La ihforie dea ph&iomdnea laminenz donne, aa contraire, 
nne explication fort simple de tons les ph^nomenes observes, en 
admettent aanlement, ce qui somble da reste Evident, qn'nne 
plaque de BenaibilitS donn^ ne peat etre impressionnce pendant 
le mdme temps qae par des lamieres possedant one intensito sa- 
perienre k nne intensite donnee : cette intensite qai dcfinira jaste- 
ment la sensibilito de la plaqae, si Ton pent mesaror en valear 
abaolne I'intensit^ limite qni donne uno impression pendant 
I'lmit^ de temps. L'etade de la diffraction aa foyer des lentilles 
&ite par Schwerd (BeugungseracJieiuuiufen), simplifi<So et etendae 
par K. Andre ('Etnde de la Diffraction dans les Instruments 
d'Optiqae' — Annates de VEcole Normale Sujycrieure, 1876, tome ▼• 
page 275), conduit aux r^ultats suiyauts. L'intensite lamineuse 
n'est pas constante en dedans mcme de 1' image goometrique: elle 
dfcroit prto des bords, et, aa bord memc, elle n'est que la moiti6 
de ce qn'elle est an centre. En dehors do Timage geometrique on 
troaye encore de la lumiere dont Tintcnsitc decroit progressiye- 
ment en tendant yers zero. Si Ton considere an objectif parfait, 
rigonreusement aplanetiquc, la largeur de cette zone de diffrac- 
tion yarie en raison inverse de rouverture de Tobjectif. 

L*aberration produit des phenomenes analogues qui se super- 
posent anx precedents et augmentcnt considerablement Tetendue 
de la zone diffractee, sans cependant changer Ic sens general 
da ph^nomene. Quaud on reduit Tobjectif on a toutefois a tenir 
compte de deux effets inyerses ; celai de la diffraction qui aug- 
mente, et celui de Taberration qui diminuo en meme temps que 
decroit I'ouyerture de Tobjectif . 

Ces lois suffisent a expliquer tous les faits observes. Qaand 
on anemente T intensite de la source, rintensite croit propor- 
tionneuement en cbacan des points dc la zone diffracteo, et la 
plaqae photograph ique, qui reste sensible pour uno intensite 
absolae determinec, donne des images de plus en plus grandcs. 
Siy an contraire, Tintcnsitc decroit assez pour que, dans le temps 
considere, la plaque ne soit plus sensible a la moitie de Tiutensite 
an centre de la plaque, on aura des images plus potites que 
Timage g6ometrique. 

An lien de faire varier rintensite, on pcut lairc intcrvenir la 
daree de pose ; on aura alors des effets analogues ti ceux que 
donnait la variation de Tintensite, mais moins rapides. En aug- 
mentant I'exposition, on rend en effct la plaque sensible a des 
lamieres de plus en phis faiblcs ; mais cette scnsibilito tend rapidc- 
ment vers une certaine limite, car rexporicnce semble prouver 
que toute intensite qui tombe au-dcssous d'unc certaine limite, 
variable avec la sensibilite de la plaque, ne pent pins produire 
d'impression meme pendant un temps infiuiment grand. 

L'influence de Touverture de Tobjectif est egalement mani- 
feste : la zone diffracteo augmente quand Touverture dc Tobjectif 
diminne, et exactement en raison inverse de celle-ci. L'experience 



392 -If. Angoty On ths Application of XXXYIL 7, 

a montr6 cette angmentation, mais tin peu moins rapide que ne 
le veut la th^orie ; en effet, en memo temps qne la diminution de 
ronvertore prodnit nne angmentation de la zone diffract^e, elle 
diminne noteblement Teffet de raberration. 

Enfin, qnsuid on sonmet a la Inmi^re difiase la plaqne sensible 
avant d'j imprimer Timage, celle-ci vient se faire snr nn cbamp 
dijk 6clair6, et cet eclairement g6n6ral masque une partie de 
Tagrandissement diffractionnel. 

En r6sum^, les faits observes sent en parfait accord aTec la 
th6orie. La dimension des images photographiques varie avec toutes 
les conditions de Tezp^rience ; mais, pour expliquer ces variations, 
il suffit d'avoir recours aux theories ordinaires de I'optique, et non 
k I'hypoth^se d'un cbeminement mysterieux des actions cbimiques. 
Dans une prochaine communication, j^ezposerai les applications 
de ces recherches k I'observation photograpbique de certains 
ph^nomenes astronomiques, notamment k celle du passage de 
Venus. 



Stir r Application de la Photographie a V Observation du Parage de 

Venus, Par M. Alfred Angot. 

Dans un precedent travail, j'ai 6tudi6 les causes diverses qui 
peuvent modifier la dimension des images pbotograpbiques, et 
montr6 que tons les faits observes sont d'accord avec la tb6orie 
de la diffraction. Je desire exposer aujourd'bui les resnltats 
auxquels conduisent mcs experiences pour Tapplication de la 
photograpbie a Tobservation du passage de Ven^is, 

Avec la metbode d'observation photograpbique, on pent 
cbercbcr a determiner par deux precedes diffcrents la parallaxc 
solaire au moyen du passage de VeniLS. i**. On cbercbe a 
mesurer Teffet parallactiqne direct, c*est-a-dire la difference des 
positions apparentes de Vemis vue au meme instant de deux 
stations eloignees. 2°, On determine seulement par la pboto- 
graphie Tinstant des contacts. Co dernier precede conduit 
identiquement aux memes calculs que robservation directe, qu'il 
ne fait que doublcr. Le premier, au contraire, est propre a la 
pbotograpbie, puisque les astronomes n'ont pas encore imagine 
de moyens surs de mesurer les distances de Vemts et du Soleil k 
un instant quelconque. 



I. Mestire directe de VEffet Parrdlaciiqta*, 

La position de Venns sur le Soleil est definie par deux 
elements : la distance des centres et Tangle que fait ia ligne des 
centres avec une direction fixe, celle de Tequateur, par exemple, 
angle que Ton ddsigno communement sous le nom d'angle de 



May 1877. Fhotography to the Transit of Venus, 393 

position. MaiSy ponr determiner la valenr do la parallaxe, il 
soffit de oonnaitre lea valeura d'une senle de ces deux quantites 
mesor^ an mdme moment en denx stations convenablement 
choisies. De 1^ denx manieres de mesnrer directement Teffet 
parallaotiqne : — 1% par Tangle de position; 2^, par la distance 
des centres. Nons aliens examiner snccessivement ces denx 
precedes. 

i^. Mesure de V angle de position, — D'apres les ph^nomenes 
que nons avons d^rits dans la premiere partie de ce travail, il 
eet Evident qne les diam^tres phoiographiqnes dn Soleil et de 
Venus seront variables aveo tontes les conditions de Texp^rience, 
intensity de la lumiere, transparence de 1 'atmosphere, dnr6e de 
poee, sensibility de la plaqne, etc. Mais si Tobjectif qne Ton 
emploie est bon an point de vne optiqne, c'est-fUdire ne deforme 
pas irr^gnlierement les imaees, tons les diametres du Soleil et de 
Venus seront ^galement alt&^s, et la position dn centre des denx 
astres ne sera nnllement cliaiig6e; la mesnre des angles de 
position devra done, en th^orie, donner des r^snltats ind^pendants 
de tontes les canses d'errenr signal^s. Mais on rencontre, dans 
la pratiqne, de tres-grandes difficnlt^s i obtenir, avec le degr6 
d'exactitnde reqnis par le calcnl, nne direction fixe servant 
d'origine anx angles de position. Les expeditions americaines 
sont, a ma connaissance, les senles qni aient cherche i r6sondre 
le probleme ; il est done n^cessaire, ponr appr6cier la methode, 
d'attendre la publication et la discussion de lears resultats. 

2^. Mesure de la distance des centres, — La position dn centre 
des denx astres n'est aucnnement modifiee, nons Tavons vn, par 
les phenomenes de diffraction qn'introdnit dans Pimage nn 
systeme optiqne suppos6 parfait. La mesnre de la distance des 
centres doit done, theoriqnement, inspirer tonte confiance, 
comme celle des angles de position. L'exp6rience, dn reste, 
aemble prouver qne les dimensions d'appareils et le mode 
op^ratoire des missions fran9aises penvent donner la distance 
des centres avec le degr^ d'exactitnde reqnis par le calcnl.* 

Mais il y a, dans ce precede, nne difficnlt^ de mSme ordre 

qne celle qni consistait, dans le precedent, a determiner I'origine 

des angles de position, c'est la ndcessito de connidtre la valour 

fingulaire des images. Les images focales sont mesnrees en unites 

de longueur ; mais, pour pouvoir comparer entre elles les ^preuves 

obtenues dans les differentes stations, il faut connaitre quel 

%ngle represeute, dans le ciel, nn millimetre mesnre snr I'eprenve, 

ou, ce qni revient an mt^me, sons quel angle on voit, du centre 

^iptiqne de I'objectif, nn millimetre place an fover. On pent, 

^u reste, determiner cette valenr de bien des manieres differentes : 

* On KG rappello quo les photographies des missions fran9aise8 etaiont 
5^tenue8 directement au foyer d'un objectif d'environ 3"*8o de foyer. Snr les 
X mages directes, sans grossissement, le diam&tre du Soleil est d'environ 35""'84 
^ eelni de VSnus de I'*"'I5. Les images ^taient obtennes en outre snr plaques 
^^Agoerriennes. 



394 • ^' -^ngot, On ilte Applicatio'i of XXXTIL 7, 

la premiere consiste a mesorer exactement la longueur focale de 
Tobjectif employ^ (proc^d^ suivi par lea Am^ricains) ; on peat 
encore placer aa foyer de rinstrament nn micrometre k fils, on 
nne plaqne de verre divis^, et noter le temps qn'nne ^toile 
connue met k franchir nne distance donn6e, qnand I'appareil 
reste fixe. Mais il paraitra pr^f^rable de determiner la Yaleor 
angnlaire des images par des proc^d^s parement photogra- 
phiqnes. On ponrra, par exemple, collimer Tinstrament pboto- 
grapbiqae par nne Innette m^ridienne, et pbotograpbier ainsi 
le reticule de cette demiere, dont les file sent k des distances 
parfaitement connues. Enfin nn proced6 employ^ depuis long- 
temps par M. Rutherford, et qui Ini donne d'exceUents r^sultats, 
consiste a dinger a former sur la plaque photograpbiqne an foyer 
de rinstmment rigoureusement immobile I'image d'une etoile 
brillante. Get astro laisse alors nne trace lumineuse continue ; 
la longueur de cette trace, et le temps pendant lequel elle a 6t^ 
obtenue, permettent de determiner aisement la valenr angnlaire de 
rinstmment. On pent encoro remplacer dans cette metbode 
Tetoile par le Soleil ; il faut alors, Tappareil restant immobile, 
prendre deux images du Soleil. a nn intervalle de temps par- 
faitement connu, et mesurer la distance des centres de ces deux 
images. II est n^cessaire, dans ce cas, que les deux images 
n'empietent pas Tune sur Vautre ; alors les diametres du Soleil 
seraient modifies dans tonte la partie commune aux deux images. 
J'ai montre, en effet, dans mon premier travail, que les images 
sent, en g^n^ral, plus petites lorsqu*elles se forment sur nn 
champ dej^ impressionne par la lumiere. 

II est, enfin, nn dernier precede qui parait irreprochable an 
premier abord, mais qui, dans la pratique, conduirait a des 
erreurs notables. J'ai montre, en operant sur des objets uniforme- 
ment eclaires, a bords rectilignes, et de dimensions tres- 
superieures a la zone de dififractiou, que Taagmentation do 
rimage d*un objet lumineux est egale a la diminution de celle 
d*un objet obscur dans les memes circonstances. La somme 
de CCS dimensions etait constante et egalc ii ce qu^elle devrait 
etre si rimage se formait seulement d'apres les lois de Toptique 
geometrifjue (voir la premiere partie). S*il en etait rigou- 
reusement de meme pour le Soleil et Vnncs, les diametres de ces 
deux astres, variables en sens inverse d*une epreuve a Tantre, 
donneraient une somme constante. Cette somme pourrait 
servir de factenr de reduction pour comparer entre elles les 
^preuves des dififerentes stations, et il suffirait des lors de deter- 
miner la valeur angulaire d'un seul instrument: le rapport des 
sommes des diametres do Soleil et de VeuuSj dans deux instm- 
ments, serait celui de leurs valeurs angulaires. 

Malheureusement on ne pent compter sur la Constance de 
cette somme, et cela pour plusieurs i*aisons : 

I**, Le diametre de Vmus est loin d'etre gi*and par rapport 
a Tetendue de la zone dififractee. La theorie montre alors que 
la diminution du diametre de Vcmis n'est pas la meme que celle 



May j877* Photograjthi/ to the Trajisit of Vmus. 395 

qui 86 prodnirait pour nn bord rcctilignc ; le Soleil, an contraire, 
a HUB conrbnre assez faible pour ponvoir etre considere comuie 
nn boid reotiligne. 

3**. L'intensit^ Inminense dcs diflerenU points dn Soleil n'cst 
pas dn tent nniforme ; elle decroib rapidomoni vers lea bords, par 
enite de la convexito et de la nature physi(][no de cct astre. Cetto 
decroissance est memo tcllcment accnsee qne Tintensito photo- 
gpeniqne des bords parait infericure a cello de la penombro des 
t-acbes. Pendant la duree du passa«:::o Vcui'fi S(? projettera done en 
nn point dn Svileil beauconp phis hiiniiicux (juo n\^t hi bord, et 
dont rintensito vaiie sans ecsso a mosurc qne Venus so deplaco 
sar Ic Soleil. Kaugmcntation du Soleil est alors difiorontc de la 
diminution de Vvnug, et la sonimo do leurs diamctres est vari- 
able avec toutcs les conditions do Toxporionco, seusibliito de la 
plaque, dnroo do pose, ti*au.sj>:iri'nc*o tlo ratinosphoro au moment 
ou Ton fait la photognipbie, etc. 

Tontes cos previsions out eU; confirmees jnir roxperience 
directo a Tappureil a passages artificiols, et, mionx (j[ue tout le 
reste, lamesurj des epreiives du pass;igo memo de Vuiuify obtenues 
dans tous les pays et* dans les cireonstaucos les plus varices, doit 
mettre ces causes d'erreur on evi«lenco et montrer quo, pour 
determiner la valour angulairo de^ instruments, il taut avoir 
recours a Tune des mJ'tnodes (jiie j'ai exposeos plus baut, en 
renon^ant completement a la r)Ustanco presunieo de la sommc 
des diamctres des deux as t res. 



II. Di'termiiiaiion de Vlnstant dcs Contacts, 

JjSi determination do Tinstant des contacts, qui pent etre 
tentee par la photographic pour controler I'observatiou directe 
8*obtient de deux famous di tie rents, so it par T observation dn 
contact memo, soit inu*rii.\ soil externa, «lt'S deux (lis«jUf\s, soit 
par la niesure dc li corde eoinmuiij :i \'r:iv.< vi au Soleil au 
moment ou la plant.*'..) cntr.' s-n- ii- \)^>v.[ ^\ • r.i-%;"t'. K:\ riudiant 
commeiit varif, nvee J • t',':a]»s, ctii* »/' >/ '.■;■' J- < cn'iics O'.i cordo 
commune, on en deJuii \hiv ••\;ia{jul:i;iij:i ie nionient oh e^'tte 
distance est nulle, e'est-c'i-dirv? le eontaet. Cjnime les causes 
d'errcur qui s'attiichoni a ces {\ii\K ])roeC'iles sont k*s meiu'js 
nons les reunirons pour \.i discussion. 

La theorie de la dillVaction pcrmot d-^ oaleulcr tontes les 
phases du passage <le la planete sur le Ixjid du Soleil ilins nn eas 
simple, eolui ou I'oa suppose que W tu-- e-Jt lorinee par nn disqne 
ou par une sphere opaque sans atinosphi're, et quo le Soleil a uru' 
intensite lumineuse constiinte en chacun de ses points. On trouve 
de la borte (pie, dans rinterieur memo dc^ la j)artie geometrique 
de rimage, I'intensite deeroit quand on s'approcho des bords, et 
fonne nnc zone estompeo qui setend bien en dehors do Timage 

G 



39* 



JIT. Attgfft, On the AppUcatiim of 



g^om^triqne. On pent aiusi obtenir par pointa nne sirie de 
covtIm de ntcMH, pour ainsi dire, tont le long desqnelleB I'intenmte 
1 amine D so est oonstanto. Ia 
-^ fif^re ci-jointe repr^scnte sn>B- 

Hitirement la forme g^n^rue de 
ces conrlioH an moment mfime 
du contact geometriqafi interne. 
La conrbc AA', tout lu long de 
Inqncllo rintcnBitv eftt la moiti^ 
de ce qn'olle eat aa centra dn 
Soleil, se confond avec le bord 
gdoraetriqae de cet aatre ponr 
tooa les points nn pen 41oign£8 
dn point de contact ; dans lea 
I regiona de Vt-nui distantea da 
I mgme point, la conrbe eat con- 
centrique a I'image guometriqne 
et nn pea inteneare (elle ne 
coincide plus avec le bord g^ 
m^triqae i. canae de la coarbare 
de Ve.nvi) ; enfin, anz enTirons 
da point de contact, cea denx 
conrbes se raccordent de fafon 
A reprodnire ezacteraent I'appa- 
rence deatgr.ee aoas le nom d« 
goutte noire on de ligament. 
Cctto apparonce est ezager^ 
j^ encore dana lea conrbes d'in- 

tonsif/' i et ^ qne represents 
I'galement la fisnrr. On obticnt di;s traces analognes ponr ehaqne 
instant dii paHsagc. 

D'antrc pnrt, tine plague photograpluqne, ozpos^ a la Inroierc 
pendant un temps determine, donno nne image qui comprend 
tons Its points dont rintonsltt'' Inminensc est snperienre k nne 
oertaiiie limite. L^impression s'arrete ii nne do ces coarbes de 
nivean (|iii- j'ai indiquoes plug hant, et comprend dea conrbes do 
niveait ill' pins cu plus faibles, iV mesnre qne Ton augmonte la 
sensihiliti' de la pinqno, I'intenaite de h Inniit'Te, et la dnW-e dp 
pose. 

Ce fioiit jnstement lea conditions dans lesqnellos ont ete 
obtenues mes pbotogmphies. L'apparcil a passages artificiels 
6tait amene a une position convenable, puis fixe, et on fnisait snr 
la meme plaque cinq eprenves Bnccessives, correapondnnt a des 
dnrees de pose progresHivemcnt croissantes. On obtient aiiist 
la forme de cinq conrbes do nivean de pins en pins faibles, et il 
t frappant de V()ir avec qnellc fidelite rexpericnce n'-alise lea 
1 indiqneeg par la tbi^orie. ^ ' 







r4p6t^e en donnant a la planete lea positions qn'elle occnpe de diz 
en diz, on de qnin^e cii qninze, secondes pendant les cinq minntea 



IImj 1877. Photography to the Transit of Venus. 397 

qui precedent le contact inteiiie d*entree et pendant lea deux 
miniiteB qni le snivent. 

Des r^nltats analogues avaient deja ^t^ partiellement, dn 
Teste, obtenns k Gh*eenwicli et par M. Janssen, dans les ex- 
periences prcliminaires faites avant le depart des expeditions 
poor le passage de Venus: on avait qnelqnefois obserr^ des 
apparences de goutte noire qaand Tappareil a passages artificiels 
etait eclair^ tres-fortement par la Inmiere directe du Soleil, par 
ezemple. 

Beste a determiner Terrenr que ces phenomenes peuvent 
introdnire dans Tobservation photographique de Tinstant des 
contacts, surtout des contacts internes. Or, la th^orie montre que 
r^parence generale ne change pas brusquoment au moment des 
contacts. Meme alors que la planete est entierement entree 
sur le Soleil, Tapparencc de la gootte noire pereiste tant que le 
filet lumineux compris entre Vcnvs et le bord du Soleil n'a pas 
une dimension egnlc on snporicure u cclle de la zone de lomiere 
diffractee. II sera done possible d^obtenir encore une gouite 
noird apres que le contact geometrique aura eu lieu : il suffira, 
pour cela, de poser tres-peu de temps. 

La photographic a, dans cette observation, un desavantage 
considerable sur Tobservation optique directe. L'oeil, eu effet, 
k c6te d'une lumiere tres-vive, comme cello du Soleil, devient 
incapable de perccToir des intensities assez faibles : la perception 
optique s'arretera done gcneralement a des courbes do niveau 
pen distantes du bord geometrique, tandis qu'en augmentant la 
sensibilite des plaques photographiques ou la duree de pose, on 
ira chercher des courbes d'intensite aussi faiblo que Ton voudi'a. 
Dans Tobservation du passage, meme avec des plaques identi- 
ques et une duree de pose constante, il suffira du moindre 
changement dans la transparence de Tatmosphere pour que 
rimpression photographique s'arrete a des courbes de niveau 
differentes, et que de deux epreuves successives la demiere 
semble correspondre a une periode anterieure du phenomene. 
Les effets indiques diminuent si Ton augmente Touverture de la 
lunette, mais ils croissent considerabloment pour peu que 
Tobjectif employe possede la moindre aberration. Avec un 
objectif non rigoureusement aplanetique, j'ai pu obtenir encore 
un contact apparent par des durees de pose tres- faibles, alors que 
Venus etait completemeiit entree sur le Soleil depuis une 
minute de temps. 

" Quant aux contacts extemes, la diffraction modifie la forme 
de rechancrure que Venus produit sur le Soleil ; mais, comme il 
s'agit seulement de constater la presence de cette echancrure, il 
est possible que Tobservation photographique donne des resultats 
de meme valeur que robsorvation optique. 

Beste un dernier mojen, qui consiste a etudier comment 
varie, avec le temps, la corde commune ii Venus et au Soleil, 
pendant Tentree ou la sortie, et a en deduire par extrapolatior. 
le moment ou cette corde est nuUe, c*cst-a-dire les contacts. Ce 

r. Cm 2 



398 3fr. Downing^ A Determination etc, XXXYIL 7, 

proc^6 pr^sente, en plLotographie, des difficult^s partioalieres, 
puisque pour on memo instant la longaenr de la oorde pent varier 
entre des limites considerables avec la sensibility de la plaqne, la 
dnr6e de pose, on la transparence de Tatmosphere. 

Tontes ces conclnsions, verifi6es direotement par I'exp^rience, 
sont d6dnites de Thypo those d'nn planote sans atmosphere, et 
de regale intensito Inminense des differents point s dn Soleil ; 
mais on doit reconnaitre que le ph6 nomine reel est encore pins 
compleze. Nous esperons ponvoir, M. Andre et moi, determiner 
experimentalement les modifications que la presence d*nne 
atmosphere antonr do Venus amcne dans les rcsnltats anxqnels 
nous conduisent nos premieres experiences. 

Eq resume, Tobservation photographique dn passage de 
Venus presente des difEcultes au moins aussi grandes que 
I'observation optique ; mais on pent conserver tout espoir 
d'arriver par ce mojen a nne bonne determination de la par- 
allaxe, surtout si Ton emploie les methodes de mesnre de 
distances de centres et d'angles de position, methodes propres 
k la photographic. En tons cas, le prochain passage de 
Mercure (Mai 1878) devra efcre observe avec le plus grand soin, 
afin de verifier d'abord sur nn phenomene celeste nos con- 
clusions, basees sur des experiences do passages artificiels, et 
d 'assignor ensuite exactement les limites entre lesqnelles les 
causes d'erreur signaiees peuvent varier dans la nature. 



A Determination of the Semi-diameter of Venus at the mean dis* 
tance of tJie Sun from the Earth. By A. W. Downing, B.A. 

In this investigation I have made use of the results of the 
Washington Transit Circle Observations during the years 1866- 
1872 inclusive; the Transit Circle having been brought into 
use in 1866, and the results of 1872 being the most recent to 
which I have access. Daring this interval the value of the 
semi-diameter of Voius at the mean distance of the Sun from the 
Earth, given in the American Ephcmeris, and with which the 
AVashington Observations have been compared, was 8'''546. 

Let the trne semi-diameter = 8"*546 (i +?/)> so that ?/ =: co- 
efficient of variable part of correction depending on tJie planet's 
distance : and let x = constant part of correction arising from 
irradiation &c. ; we have then a scries of equations of the form 

X + t/ X Tab. Somi-diiimetcr = Correction to Eplicmoris. 

Using all the observations of vertical diameter of Venus 
made during the above-mentioned years, I have formed 167 



Hay 1877. Messrs. Wilson and Bedbrdke^ Caialogue etc. 399 

equations in this manner ; solving these by the method of least 
squares, I obtain the equations — 

1674?+ 1636-3^ « 403 
1636-34?+ 23565-24^ « 239- 1 1 ; 
whence 

dp - 04439 ±oio36x<;, 

where e is the pr obable error of an observation, and 

y ■■ — 0*02068 ± 0007 7 7 X e. 
Therefore 

True Scmi-diametor = 8"-546 (i +^) = 8''*3693 ± 0*0664 x e. 

The valne 8"*^46 was determined by Prof. Peiree from 30 
observations made with the Washington Mural Circle dnring 
the year 1846. 

22 Waterloo Boad, Dublin, 
1877, May 9. 



&co?id Catalogtie of Micromeirical Measuremenia of Double Stars 
made at the Temple Observatory. By J. M. Wilson, M.A., 
and G. M. Seabroke, Esq. (Abstract.) 

This Catalogue contains the measures made at the Temple 
Observatory during the years 1875 ^^^ 1876, and somo few 
'^^asures made in previous years that were omitted in our first 
Catalogue. 

^ Most of the measures were made by Mr. Seabroke, Mr. 
'■^ilson having been unable to work at the Observatory during 
'^75 and part of 1876. Mr. Scabroke's measures were, how- 
®^^r, frequently confirmed by those of ^Ir. Percy Smith. They 
J^'^re all made with the parallel wire micrometer, and a magni- 
^y^xig power of about 400 on the Alvan Clark refractor of 
^ inches. 

^^ The Temple Observatory is now being built in a permanent 
^nn, with a Curator's house adjoining, and we take this op- 
I^^itunity of a break in our series of measurements to offer this 
*^<5ond Catalogue to the Society, in the belief that double-star 
'^^^asures are more valuable when published at frequent intervals. 
We thought it unnecessary to print the R.A. and Dec. of 
^trnve's stars. All observers who are likely to use this catalogue 
'^ill have them at hand. 



400 Serior ArcimiSf Lunar Eclipse etc, XXXTO. 7, 

Lunar Eclipse of the 2'jth February, 1877, observed at Cadiz. 

By Angusto T. Arcimis. 

I have long delayed reporting my observations of this eclipse 
because I even doubted the reality of what I had seen, but 
having read in the scientific journals that the phenomenon had 
everywhere presented a similar aspect, I venture to offer the 
result of my observations, which can no longer be received with 
doubt or mistrust. 

The Sun set at 5** 35". The clouds which gathered in the 
east prevented my seeing the Moon until 6^ 20™ ; it was already 
eclipsed, and in spite of the crepuscular light, the characteristic 
copper tint was, though faintly, visible in the centre of the dink, 
the other portions being covered by the clouds. 

At 6^ 46™ the Moon is red throughout to the naked eye and 
presents the appearance, were that possible, of an annular 
eclipse ; the centre is dark and not a single detail of its surface is 
distinguishable ; it is surrounded by a luminous fiery corona. This 
strange aspect disappears through the telescope, and the eclipse 
presents the normal appearance. 

The clouds now and then interrupt the observation. 

At 7'^ the red ring breaks towards the south, and the inroad 
of the shadow becomes distinctly visible to the naked eye. 
Through the telescope only the western edge, surrounded by the 
penumbra, can be distinguished, while the rest of the disk pre- 
sents a dull grey colour so deep that it effaces every detail of the 
lunar surface. 

The clouds again invade the sky. 

At 7'* 41"* it clears partially, and the crater Grimaldi emerges 
from the shadow. 

At 7** 49™ emersion of Kepler. 

At 7** 57™ „ „ Kopeniinis. 

At 8** o™ the shadow crosses the centre of Flatu. 

At 8*» i°* emersion of Tijcho. 

At 8*^ 5"* „ „ Archimedes. 

At8»» 7»" „ „ Ftolemeus. 

At S^ ii"* „ „ ManiUu.<. 

At8^»i5°> „ „ Menelaus. 

At 8** 2i"» the line of the shadow reaches the crater Endy- 
mion and the edge of Mare A ustrale. 

At 8^ 28™ the shadow touches the edge of Mare Crisium. 

At 8^ 36™ the last contact takes place at 90° from the boreal 
pole towards the west. 

This eclipse presented a notable aspect, and the corona of red 
light which spread over the internal edge of the Moon elicited 
the admiration even of strangers to the science. An unforeseen 
circumstance prevented my using the spectroscope. 



Hfty 1877. 



Sir 0. ShcuJtoell, A Table etc. 



401 



A Table for faeUiiating the determitiatioii of Mean Equtnvclial 

Time to the end of the present Centary, 

By Vice-Admiral Sir Charles Shadwell. 

In the Nautical Almanac, from the year 1834 (the date of its 
first appearance in its present improved form) up to 1875 in- 
clusive, information was formerly given, at page 20 of each month, 
to facilitate the determination of * J^Iean Equinoctial Time.* 

From and after 1876 this information has been altogether 
discontinncd. No reason has been assigned, either in the 
' Annual Prefaces ' or in the * Explanations ' of that volume, for 
this omission. It is, however, understood to have been with- 
drawn because it had never come into general use among 
astronomers, as had been anticipated at the time of its first 
introduction. 

Since the use of equinoctial time afforded a means of 
reckoning time free from the necessity of specifying any par- 
ticular geographical locality, being measured from an epoch 
common to all the world (viz. the passage of the mean Sun 
through the mean vernal Equinox) and identifiable indepen- 
dently of all localities, thus avoiding all ambiguities in its 
description, its disappearance from the pages of the National 
Ephemeris is, I think, to be regretted. 

With a view to rectify this omission to a certain extent, and 
to afford those desirous of employing equinoctial time the 
means of doing so in future, the accompanying Table, giving the 
data for its determination up to the cud of the present century, 
is herewith submitted to the notice of the Royal Astronomical 
Society : — 



Tabu for fncilUating tftf determination of Mean tjinmfjctUd Timr. 



Equinoctial 
Year. 

1875-76 


Date of 
Conimcncomcnt. 

March. 
22 


Number. 

81 


I'nicLion of I>niinoctlal 

Time for till- Year to 

1)0 added ro the 

Equinoctial Day. 

d 

0-574169 


1876-77 


21 


81 80 


0-331953 


1877-78 


21 


So 


0-089737 


1878-79 


22 


81 


0S4752I 


1879-80 


22 


Si 


0605305 


1880-81 


21 


81—80 


0-363089 


1881-82 


21 


80 


0-120873 


1882-83 


22 


81 


0878657 


1883-84 


22 


81 

• 


0636441 


1884-85 


21 


81—80 


0-394225 



402 



sir C. Shadxoell, A Table etc. 



XSTTtt. 7, 



Eqninoctial 
Year, 

1885-86 


Datoof 
Commencement. 

March. 
21 


Kumbcr. 
N. 

80 


Fraction of Equinoctial 

Time for the Year to 

be added to tbc 

Eqnlnoctial Day. 

d 

0*152009 


1886-S7 


22 


81 


0-909793 


1887-88 


22 


81 


0667577 


1888-89 


21 


81—80 


0-425361 


1889-90 


21 


80 


OI83145 


1890-91 


22 


81 


0940929 


1891-92 


22 


81 


0-698713 


1892-93 


21 


81—80 


0-456497 


1893-94 


21 


80 


0*214281 


1894-95 


22 


81 


0-972065 


1895-96 


22 


81 


0-729849 


1896-97 


21 


81—80 


0487633 


1897-98 


21 


80 


0-245417 


1898-99 


21 


80 


0-003201 


1899-1900 


22 


81 


0760985 



Explanation of the Table, 

This Table contains for the equinoctial years named, that is 
for the years 1875-76 to 1 899-1900 inclusive, ist, in column 2, 
the day on which the equinoctial year commences ; 2ndly, in 
column 3, the number N ; 3rdly, in column 4, the fraction of 
equinoctial time to bo added to the day of the equinoctial year. 

N is the number of days which is to be subtracted from the 
*day of the year' (increased if necessary by 365) to give the 
correspondiug day of the equinoctial year ; the day of the year 
correspondinp: to any given date being taken from the Table pul>- 
lished annually in the Ntiutical Almanac commencing with 1876 
(* Day of the Year,' <fcc., pp. 484 &c.) 

This number is generally 81, but sometimes 80. When both 
nnmbers are given, 81 is to be subtracted from the day of the 
year between the vernal Equinox and December 31, and 80 
between January i of the following year and the sncceeding 
Equinox. 

Applicaiion of the Table. 

I. To find when the equinoctial year commences : — 

To the date in column 2 add the complement to unity of the 

fraction in column 4. 

Thus the equinoctial year 1884-85 commences on ^larch 

2i'^ + (i — 0394525), or on March 2i<^-6o5775 Greenwich Mean 

Time. 



Maj 1877. Mr, PenrasCf Description etc, 403 

So again the equinoctial year 1894-95 commences on March 
22*+ (i— 0*972065), or on March 22*^027935 Greenwich Mean 
Time. 

II. To find the mean equinoctial time corresponding to 
Greenwich mean noon on any given day : — 

From the day of the year, increased if necessary by 365, sub- 
tract the number X, and affix the fraction for the year from 
column 4. 

Thus : Required the equinoctial time at Circenwich mean 
noon on J^Iay 13, 1878. 

Here the day of the year corresponding to May 13 would bo 
132, and in the equinoctial year 1878-79 N is 81, and tho 
firaction of equinoctial time o**'84752i. 

Therefore, i32<*— 8i<*+o**-84752i ; or 1878^ 5i<*-84752i is 
the mean equinoctial time at Greenwich mean noon on the day 
in question. 

Again: What will be the equinoctial time at Greenwich 
mean noon on February 5, 1893 ? 

The day of the year corresponding to February 5, 1893, ^^ 
35, and in the equinoctial year 1892-93, X between January i 
and the following vernal Equinox is 80, while the fraction of 
equinoctial time to be added is 0^*456497. 

Hence, 35* + 365<*—8o<* + 0^*456497, or 320<^*456497, is the 
mean equinoctial time at Greenwich moan noon on February 5, 
i^93> which is required. 

Note. — Should it ever be deemed expedient to reintroduce 
"mean equinoctial time" to a place in the Nautical Almanac, 
it would not be necessary to assign 1o it a column in a page 
for each month, as under former arrangements previous to 1876. 
All that would be requisite would bo to give, in a note at the foot 
of the Table " Day of tho Year, &c.," the number N and tho 
fraction of equinoctial time to be employed, both before and after 
the vernal Equinox of the current year, with a brief explanation 
of how tliey were to be applied ; this last being given in the 
" Explanation of the Articles " at the end of the work. 

A very slight alteration of the present arrangement of the 
type in the Table i-ef erred to, and a corresponding brief addition 
to the "Explanation," would pennit this. 

Meadowbank, MelkthaWf 
1877, -^pril. 



Description of an Improved Diafjrara for the Graphical Solution of 
Spherical Triangles, applicahle to the questions arising out of 
tJie Spheroidal Figure <f the Earth, treated in the Paper read 
before the Societij Nov. 10 ult., and further illustrated hy the case 
of ike Prediction of Occultations, By F. C. Penrose, Esq. 

The Table, which should have accompanied the paper referred 
to, giving the values of n — ^namely the distance between the centre 
of the Earth and the foot of the normal in different latitudes — and 



404 Mr, F&ivrose^ DescripUcn xxxrn. 7, 

for tlie correction of the Tabular Parallax when referred to the 
game point, is as follows. The Horizontal Eqnatoreal ParaUaz 
is taken as equal 57'. When more or less than this, the figarei 
below should be adjusted proportionably : — 

Correction to Goneotion to the 

lAtitade. Polar Distance. Booeloceel H.P. 

Subtract from P.D. Add to H.P. 



5 3-OI O-IO 

10 401 o'35 

15 5 97 080 

20 789 1-34 

25 974 2-06 

30 1152 2*88 

35 ^322 380 

40 1481 4*75 

45 "6-29 576 

50 17*64 676 

55 18-85 77a 

60 1993 8*6o 

65 2085 9*40 

70 21*61 10*15 

75 222 1 1070 

80 2265 11-15 

85 22-90 11*40 

90 22-99 11*49 

The diagram attached to the paper referred to, although it 
answers its purpose sufficiently well for working the spheroidal 
corrections, is not so well adapted for the general solution of a 
spherical triangle, because the lines representing the different 
zenith distances diverge so much from one another that it 
becomes troublesome to interpolate, and it offers but little 
facility for the converse problem of obtaining altitudes from given 
hour angles and polar distances ; moreover, when the angle at the 
Moon is small, it does not suffice for determining the angle with 
sufficient accuracy. 

The new diagram avoids these imperfections. The arrange- 
ment of the lines due to the different zenith distances is much 
more equable, so that interpolations can be effected with tolerable 
certainty. 

This also applies to the interpolations required for using a 
diagram prepared for a particular latitude for latitudes within a 
few deerees of it. 

If diagrams similar to the one submitted were made for every 
fifth degree of latitude, they would suffice, as I find by trial, 



tCqr 1877 of an Improved Diagram etc, 405 

within limits of error of about 30', to determine any zenith dis- 
taiice from a given hour angle and polar distance, or for per- 
forming the conyerse operation of finding the hour angle or 
polar distance from the other two given data: and with more 
accnracj, of course, if a larger scale were adopted. I exclude, 
of conrse, unfavourable cases ; such, for instance, as are produced 
by ill-conditioned triangles, which would even be avoided when 
bgarithmic calculation is used. 

This diagram belongs to latitude 51° 30', and is, in fact, a 
projection of a sphere on a method not much unlike that of 
Mercator. It gives the relation between the three sides of a 
spherical triangle and one of the angles. Two of the sides and 
the angle may vary indefinitely, but one side is constant for the 
particular diagram. The angle referred to is adjacent to the 
constant side. For instance, if the constant side be supposed to 
be the co-latitude, the vertical measurements give polar distances 
and the oblique curved lines give zenith distances ; but for 
general use I speak of the latter as the base, and the former as 
the side, and of the angle as the included angle — that is, included 
between the constant and the variable side. For instance, it will 
be seen by inspection of the diagram, that if we combine the 
vertical line drawn downwards from VI** or 90® on the upper 
Horizontal row of figures with 50° drawn across from the verti- 
cal column on the left, they will meet very near to the oblique 
line representing the base 60^. This, using the notation given 
above, is stated thus : — 

The side 50^ and included angle 90° have approximately for 
their base 6o^ (This is true for 59** 48'.) 

In a lunar triangle, we may thus obtain approximately the 
zenith distances of the Moon and star, and the parallactic angles 
of the two bodies. For this purpose generally two diagrams 
^ be necessary, one adapted to the latitude and the other to 
the lunar distance. The following case, however, has been 
chosen as adapted to the one diagram herewith submitted. 

In the figure below, if PSM, PZM be supposed to represent 
the measurements requisite for a lunar distance observation, the 
observer may be supposed to know 

PZ The co-latitude ; 

PM The Moon's polar distance, by computation ; 

PS The star's „ „ 

SM The lunar distance, by measurement ; 

ZPM The Moon's hour angle, by computation ; 

ZPS The star's 

y^ Vrhat are required are the two parallactic angles, viz. 
r>^Af and ZMS, and the sides ZM and ZS, and also the angle 
^"^6. The two sides indeed may, under favourable circum. 



^^*^oe8, be observed ; but it is often impossible or inconvenient 
L ^^ so. The diagrams enable all these quantities to be obtained 
^^ inspection with sufficient accuracy for general purposea, wid^ 



4o6 



Mr, Penrose^ Description 



xjxnu 7; 



should more exactness be required, the solution by this means 
offers a valaable check. 

Thus all the data required for clcanng the lunar distance 
maj be determined. 

Should the azimuth be required, it may be got, muiaiit 
mtUandiSj as readily as the parallactic angle. 

The simplest way of disposing of the spheroidal correction is 
by at once referring both the observation and the lunar triangle 
to the foot of the normal. When this is done, the geocentric 
lunar distance given in the three-hourly Arguments of the 
Nautical Almanac is, for any other latitude than the equator, too 
large or too small according as the angle PMS-is acute or obtose, 
and the excess or defect = n cos D cos M, where n is the quantity 
given above in the Table for the correction of the Moon's de- 
clination, and M is the angle PMS. 

It seems, however, on several accounts more convenient to 
make this adjustment upon the measured distance, instead of 
the tabular argument, but in the contrary direction, so that 
when M is acute the distance must be increased, and decreased 
when it is obtuse, by the amount above stated. 

As respects the increment to the parallax given in the Table, 
it should receive its due proportion when the parallax in altitude 
is computed. 

As an example of reducing a 
lunar distance with the help of the 
diagram, let it be supposed that 
the altitudes have not been mea- 
sured, but the distance only. 

Then, in the lunar triangles 
PZM, ZMS, after computing the 
hour angles and polar distances of 
the Moon and star, wc have — let us 

SU])pOSC — 




62-30 



rz = 38 


30 


rM = 62 


30 


SM = 38 


30 


rs » 98 


32 


SPM = 14 


15 


SPZ = 51 


45 



In the spherical triangle PMS 
tho use that is made of the given 
side SM is in the selection of tho 
proper diagram, and the samo 
applies to the use of the side PZ in the spherical triangle PZS. 

Then, combining 62° 30' as a side with 98° 32' as a base, we 
obtain the included angle 157°. This is the angle PMS. 

Then, in triangle PZS, using qS"* 32' as a side and 51° 45' as 
an included angle, we obtain for the base PS 74*^ 30'. 



Hay 1 877* of an Im^trjved Diagram etc, 407 

Then, in triangle PZM, using 62** 30' as a side and ZPS + SPM 
s66^ as an included angle, we get for the base 54°. 

Then, in triangle ZSM, with 74° 30' as a side and 54** asa base, 
we obtain the star s parallactic angle ZSM = 50** 30'; and lastly, 
in the same triangle, using 54^ as a side and 74^ 30' as a base, 
we obtain ZMS, the Moon's parallactic angle =112^. 

The corrections may now be made. 



21 



The effect of the increased ralue of parallax in altitude^ 
= 7" sin 54° cos 112**, increasing the dibtauce by ./ 

But the distance must be decreased, on account of the^ 

term h cos D cos PMS, by J . 

— ^ 

Total correction 13-2 

This example is not an imaginary case, bat would have occurred 
in latitude 51° 30' S. and longitude 4*^ 34™ W. on Feb. 9th 
nit. in the distance of a Aqullce given in the Nautical Almanac, 
As the parallax then was 54', the amount above given must be 
reduced to 12" 6. But this quantity would have affected the 
loagitade by 52^ and by more than 8 nautical miles in distance. 
And this is bv no means an extreme case. 

I showed in the former paper how this approximate deter- 
mination of the altitudes and angles, &c., might serve to 
fecilitate the accurate clearing of the lunar distance. I will 
proceed to show how it can be used to assist in predicting 
occultations and eclipses. At the bottom of the diagram is 
^ded a scale of logarithmic sines similar to that used on the 
slide rule, which will enable opposite sides or angles to be ascer- 
tained without i-ccourso to another diagram. 

As an example of its use, take the figure already given, and 

^ the triangle PZM let it be required to find the angle PMZ. 

Since log sin PMZ — log sin PZ = log sin ZPM— log sin ZM, 

the difference on the logarithmic scale between PMZ and 

3^*^ 30' must equal the distance between ZPM and ZM. Mea- 

^^re then the interval between 66° and 54° on this saale and 

*pply it to 38° 30', and it will be found to reach to 45°, whicli is 

^ery nearly the true result. It should be observed that when 

tao angles approach 90*^ this scale is not suited for accurate dc- 

^^^^ination. At such points, however, the diagrams are at 

^*^®ir maximum of efiiciency. 

Per the purpose of predicting occultations, an additional 
^*^;?ram is prepared with certain requisite scales, especially one 
^^ niinutes of arc for different values of parallax. It is suitable 
^^ all latitudes. 

Having prepared the proper elements, lay down the Moon's 
bourse on the occultation diagram, and, with the hour angle and 
P^>lar distance, find, on a diagram of zenith distances suited to 
"® latitude, the zenith distance and parallactic angle at the 
J?^'»ieiit of conjunction : the former is required for ascertaining 
. ® ^JUiount of the Moon's parallax in altitude, and the latter for 
direction with reference to the point C, which represents the 



aqS Mr, Penrosej JDescri^tion etc, xxxvn. 7, 

centre of tbereartb, or rather the. foot of the normal belonging 
to the latitude. 

When the position of the place for which the prediciion is 
made is laid down for the moment of conjunction, it is seldom 
difficult to decide in what part of the Moon's path the pheno- 
menon is to be looked for ndthin an hour. Make, then, a new 
computation of the parallax in altitude and the parallactic angle, 
and lay down and join the points which have been determined. 
A scale is given for dividing any hourly segment of the Moon's 
path into 30 subdivisions, and there is little difficulty in 
dividing a corresponding hour interval on the line joining the 
two places of the terrestrial observatory [a segment always of 
an elongated ellipse, and which, it may be observed, is genendlj 
concave for north and convex for south declinations] into 
intervals representing 10™ each. It is now easy to see which of 
the corresponding intervals are separated most nearly to the 
extent of the Moon's semidiameter, and what minute of time 
offers the best prediction. An example is given, namely, a pre- 
diction of the occultation of p Leonis Jan. 30, 1877, for 
Greenwich. 

EUmfnts of Occultation. p Leonis^ Jan. 30, 1877. 
Prediction for Greenwich. 



h m ff 
G.M.T. of <{ 12 5 II 




* '8 R.A. 

h m s 
10 26 22 


aJf'sDec. 

APprox. 

/ 

9 56 


Geooratrie 

diff. 
/ // 

27 36 


I 59 


_^'^ 






—0 18 to normal. 


20 39 18 


27 18 


G,S.T. of </ 8 46 28 




Hour an 


igle 


I^ 40" 




Parallax. 
/ // 


Observer west of Moon. 




geocentric 60 52 










+ 07 




60 59 

/ // 




Moon's Motion 


in R.A. 


34 10 




Eastwards 




33 50 




And 


in Decl. southwards 


16 8 



With these measures of the Moon's motion lay down the 
Moon's course upon the occultation diagram, and HO will be 
the Moon's course during the hour preceding conjunction ; 
and with the hour angle and declination above given obtain 
from the general latitude diagram, using them as an included 
angle and side, the zenith distance at conjunction. 

This appears to be . . . , 46 30 

The logarithmic sine scale will then '\^ ^ 
give the parallactic angle, about i " 

The parallax 60' 59'' set off upon a radius drawn at an 
angle of 46® 30' from CZ will reach to a. 



May 1877. '^' ^ Bo'eyOn a Mercurml Jieflectof. 490 

The horizontal distance from a to ZC will be the parallax 
in altitade. 

Set this off as CA, making an angle of 21^ 30' with GZ. 

A is the observer's place at conjunction. 

It is at once evident that t}ie Moon's disappearance must have 
taken place more than an hour before conjanction. Take, then, an 
hoar angle of 3^ io°> or i^ honrs before c5) and with this as an 
indnded angle, and with the star's polar distance as a side, 
lework the observer's place. This will now be found to have 

o 

Zenith distance about 56 30 
ind 

Parallactic angle . 33 35 

With these measures determine Ch and CB in the same 
manner as Qa and CA were done before. B is then the observer's 
place i\ hours before conjunction. Join AB — remembering 
that it is a portion of an elongated ellipse. Measure backwards 
upon the Moon's course "Qh = ^ HO, and h becomes the Moon's 
place corresponding to B. By means of the diverging scales 
on the drawing, the line AB may be divided into 9 divisions 
each measuring 10 minutes, and H/i into 15 divisions each 
measuring 2 minutes. Having marked off as many of these 
diyisions as may seem requisite, take the Moon's semidiameter 
mited to the parallax 60', and it will be found to reach across 
tad bridge the interval between the two points on the lines Jih 
jBid AB due to the time i** 14™ approximately before con- 
janction. By working in a similar manner the interval for the 
nappearance, it might be shown to agree most nearly with the 
time 8 minutes before conjunction ; 

These Greenwich times therefore are 10 51 

and II 57 

These predictions are identical with those given in the 
Xott^aZ Almanac^ but are quite independent of it. 

If the angle at the Moon's vertex for the observation is re- 
<inired, join the centre G with the observer's place at the time of 
^e phase in question, and having drawn a circle representing 
^be Moon, draw a straight line through its centre parallel to the 
former one. It will cut the Moon's circumference at the proper 
points for estimating the angle required. The figure gives the 
^t image, and must be allowed for accordingly when re- 
quired for the inverted image. 



^ a Method of Destroying the Vibrations in a Mercuridl Reflector. 

By M. de Boe, of Antwerp. 
{Communicated by Capt. Wm. Noble.) 

d* kf' ^ ^^ (Anvers) pense avoir perfectionn^ le systeme 
<>PBervation des fils do la lunette meridienne sur le bain de 



410 General Met^e, A CoMtnivtion of "XStvu. 7 

II emploie niip cuvette a ti-ois visc,i'.cinto=i, an fond do laqo'ilo 
il place line pla'^-.iA (l^injiTit-iine, sur kiiuuilo il laisse tombor 
([nelqnes gonttes Je nicrcara. A Tnide do cti precede lea TibratiosH 
fiont A peii pros comjilt-teoiont nnniili;es. 

Lft cavelte est k t'ond plan. , 




Arant de laisscr fomber !e mercnre sur la plaqne dagner- 
rienne, on la, frotte avec le doigt et un pen de mercure ; alors le 
fond da liquide devient plu)! adherent, co qni est la principale 
canBe qni empSclio les vibrations. 

It will be seen thiit tlio method of M. de Bo^j is merely n 
modification of tliat detwribed by Prof. PHtchard before the Boja 
Aatronoiaical Society. {Moittldy XuliGei, vol. xiii., Jan. 1853, 
pp. 61-66 ; Bee also vol, xxxri., Dec. 1875.) — W, N, 



On a Method of tnaking a Pendulum swing in an appnximaUh -^ 
Cycloidal Arc. By General M C. ileigs, U.S.A. 

I have been amnsing myself by making a " Baily compcn^:^ 
sating seconds peudnltuii "' for an old clock. 

On hanging it for tlio firsl liuif I notice that it twists i ^ 
swinging. The twist is synchronous' with the vibration oE tlr M 
pendulum, im.l iit \\\c middle of l)iu vibration, whpii the \.i-ix- ■ 
dulum is vciiicnt, its suspending sprinf* is fliit anil .straij^h^-J 
The twisted sprins; IH shorter than the Ibt one, luid this twislirj«- 
tliereforc shortens the riidius of curvature of the arc disfribc:^ * 
by the centre of osdllation after it, passes fhe vertical on eac» — 
side. 

By fnitahly proportioning the width and thickness of ( ^ 
Buspendinir sprinir, this sliorteniiig of tlie radius might i>e 
regulated that thu iirc described would be very nearly, and 
tlie work is perfect uceuratcly, cycloiilnl. 

The twist may be giwii by making the crutch strike a rou^^ 
bar placed in front of tlic pendulum rod, and not in the phine 
vibration : the further tbia bar whicit receives the impulse^— 
from the plane of the pendulum, the greater the twist. 



ifey i«i7- 



n§ a Cifcloiddl Pendvlwru 



411 



There are, then, two means of regolating the carvatare of 
the aro, yiz, : — 

I. Widtii and length of snapension spring, or, when two 
panlleL aprings are naed, the distance hetween them. 

af. Distance from the bar which receives the impulse, to the 
plane of the pendnhinu 

I have never seen these arrangements noted in any publication 
on the pendnhim, and if not heretofore tried, I think it might be 
well to try them. Hnygens' oycloidal cheeks foiled to secure 
saperior aocnraqy. 

The ordinary sui^nsion spring probably causes the pendulum 
to swing in an approximately oycloidal arc, yet it is not generally 
exact. 1 think this twisting motion can be made to produce an 
absolutely isochronous motion through the greatest ordinary or 
neoessaiy range of change in the arc of vibration of the pen- 
dulum of the astronomicfd clock. 



iKmsu Bumiriiov sphiko. 



SDiouB BPsora Bcupmaiu y 




I'iy II 




BOBIZOXTAL OCTIOV. 



HOSBO!ITAL BKTIOX 




s 

"3' 



Ronnd Bod 
in Cmtch. 

Cnitcb. 




Fendnlom 
Rod. 



Cratch 
Bod. 



This regulates aiid 
limiU the t^-ist. 

These sketches illustrate constmctions suggested. There is 
a wide range in the disposition of A, B, and C. 

Quariermtuter-GeneraVB Office, 

Washifigtoriy April 12, 1877. 

}{ H 



412 Mr, Oill, On the OpposiHon xxxni. 7, 



On the Oppoiiiian of the Minor Planet Melpomene as a means of 
determining the Solar Parallax. By Mr. David Oill. 

The accompanying list contains the Stars of Comparison to 
be observed with Melpom^ie, The same remarks apply to them as 
to the case of Mare and Ariadne, for which the comparison stars 
were published in the last number of the Monthly Notices, 

In the case of MeLpomene the necessity for Meridian observa-. 
tions of the comparison stars is specially urgent, because from 
lack of suitable stars a very rigid system of heliometer triangula- 
tion cannot be arranged. 

I am indebted to Dr. Auwers of Berlin for the daily places of 
the planet, by which I have been enabled to select the stars of 
comparison. 

I had also intended to observe the planet Iris, but this could 
not be done advantageously without taking up a new station in 
about 20° N. latitude. The circumstances of the opposition of 
Melpomene are so little less favourable than Iris that the risk and 
loss of time incurred appeared to more than counterbalance the 
advantages offered by the somewhat nearer approach of Iris, 

The circumstances of the opposition of Iris, are, however, 
very favourable for the application of Dr. Qalle's method, and 
it is to be hoped the opportunity will not be lost. 



¥ayi877. 



o/Mdpomeike ds a JIpfMi ^:. 



41* 



• 





+ + + 


■*■ 


ao 

1 ■ • 


e 

D 

.3 


■«1 




»* t JS 

^o **« (^ 






t^oo 00 00 



0000 00 



3 



f 8P : .^/^ 



: ^ 
• 00 



: * 





to 






|S5 


|a«» 


00. 


QQ 


55|b 


S \o 





M 


« . 


^ 


00 




CO 


r^ 


CO 



00 



■to 



iS 



00 



f •« 



10 <^ 

00 «4 

%0 ^^ 



as 



00 



00 
I 



T 00 OS T 
00 00 



ov T 00 00 



0<l 



. I 






p 00 

a- 

c. 






00 






vo 



N 



NO M 



ON 

to 



NO 



ro *• 



s 






? 


% 


M 


*• 


w 





+ 



« « N 



00 ^ 
ro ««*• 



ro 
ro 



OS 00 
fO 









o 

ro 



CO 



fO ro 



to 

fO 









.•o 



*^ >» 5»i -8 



H H 2 



414 



Mr. OiUf On the Oppoiiium 



iarrB.1, 



o 

mm 
+ 

V) 

V 

a 



00 




00 



t^ 00 



t I -^ 



R 8 



0\ OS 



" t 



00 









do M 



V6 00 




00 



• "8 



OS 






(^qc Sp ov Oi o^ 

l^all «i oi " 



O^ 0^ Q^ 

"^ "^ ^ ^ S 



+ 



c .0 

5 oo 

C - 

a 






M tOO^OO 0^-^0 
in N »0 ro »0 »0 



N 

m 






(i M O M M M 



r^ 






% 






OS ^O M NO 00 
N lO ^ ^ 



o\ 






a SO SO 00 
to fO «^ 



? 



»n On 0» **> SO 00 
^ ^ ^ u^ m m 




-- 8 



|(aj 1877. ofMdpomene n$ a ^ieans ete. 415 



rUm o/Hdiomdrio TnoMguUUiim of Stan to be compared with Melfomene, 



sun. 
a-3 


8-8 


A.B.of 
Middle Point, 
b m • 

4 17 38 


Dec. of 

Middle Point. 

e 1 

+ 2 29 


Podtion 
▲ogle. 
e 
341 


t)ift. 
# 
35 


a-h 


8—8-9 


19 51 


2 26 


297 


87 


3-6 


8-8-9 


20 14 


2 9 


275 


66 


3-y 


8—7-8 


18 50 


I 29 


344 


89 


7--* 


7-8-8-9 


21 t 


I 26 


208 


90 


y-^ 


7-8—8 


23 27 


46 


270 


"4 


*-c 


8-9—9 


24 52 


2 39 


228 


98 


h—d 


8-9-8-9 


25 55 


I 39 


298 


118 


h-i 


8-9-8 


24 50 


I 26 


318 


108 


t-d 


8 8-9 


28 19 


59 


232 


41 


%—€ 


8-9 


28 56 


' ^l . 


208 


107 


3-/ 


8-8-9 


30 


1 20 


231 


107 


»-^ 


8—8 


30 57 


045 


271 


III 


dr^ 


8-9-9 


30 I 


I 46 


195 


71 


d-f 


8-9-8-9 


31 5 


« 33 


230 


66 


d-9 


8-9—8 


31 59 


I 44 


230 


102 


d—h 


8-9—8-9 


32 16 


I 26 


251 


91 


d^i 


8-9—8-9 


32 59 


I 41 


241 


123 


rf-€ 


8-9—8-9 


33 2 


I I 


280 


III 


<?— y 


8-9-8 


32 2 


57 


289 


83 


/-^ 


8-9-8 


33 40 


2 6 


229 


35 


/-A 


8-9—8-9 


33 57 


I 47 


292 


38 


f-i 


8-9—8-9 


34 40 


2 2 


253 


59 


f-k 


8-9—8-9 


35 50 


2 10 


251 


97 


/— 


8-9—8-9 


34 43 


I 23 


317 


85 


A-y 


8-9-8 


33 43 


1 19 


338 


76 


y-A 


8 8-9 


34 51 


I 59 


346 


38 


• 

y— t 


8—8-9 


35 33 


2 14 


281 


31 


y-* 


8—8-9 


36 44 


2 21 


263 


66 


y-« 


8—8-9 


35 37 


I 35 


339 


91 


y y 


8 8 


34 36 


1 31 


359 


93 


«-/ 


9 — 8-9 


31 42 


2 7 


309 


41 


«— y 


9-8 


32 36 


2 18 


273 


59 


«— A 


9-8-9 


32 53 


2 


301 


79 


• 


9-8-9 


33 36 


2 16 


276 


89 


^~rt 


9-8 


4 32 38 


+ 1 32 


328 


»i3 



4t6 



Mr. CKlt, On the OppoiUton 



luvu. 7i 



Stan. 


Mag. 

8-8-9 


A.R.of 
Middle Point, 
h m • 

4 34 54 


Beo.of 

Middle Point. 

e 1 

•f I 12 


Podtioii 

Angle. 



187 


Dist 
56 


^-» 


8—8-9 


35 36 


I 28 


198 


92 


y-* 


8-8-9 


36 47 


I 35 


184 


119 


y— « 


8—8-9 


35 39 


48 


255 


31 


A— i 


8-9—8-9 


35 51 


I 56 


215 


37 


A X' 


8-9—8-9 


37 I 


2 3 


231 


72 


A— € 


8-9—8-9 


35 54 


I 16 


334 


53 


•-* 


8-9—8-9 


37 44 


2 18 


248 


38 


t / 


8-9 8 


39 51 


2 6 


276 


100 


• 

t € 


8-9-8-9 


36 37 


I 32 


359 


79 


f— A 


8-9—8-9 


37 47 


» 39 


200 


99 


f— / 


8-9—8 


39 55 


t 26 


«35 


ti9 


f— «l 


8-9-7 


40 33 


54 


268 


"7 


*— / 


8-9—8 


41 2 


2 12 


291 


68 


*--»l 


8-9-7 


41 40 


I 41 


317 


122 


*— « 


8-9-8 


42 23 


2 2 


294 


"4 


/— f» 


8-7 


43 48 


I 28 


343 


67 


/— #1 


8—8-9 


46 28 


2 30 


239 


"5 


i-o 


8-8 


46 29 


I 56 


275 


100 


^— X 


8 8 


44 30 


I 49 


299 


46 


Wi — © 


7-8 


47 7 


I 24 


236 


98 


w— or 


7-8 


45 9 


I 17 


207 


48 


* — n 


8-8-9 


47 48 


2 18 


216 


100 


X — 


8—8 


47 50 


I 45 


258 


61 


— r 


8 8-9 


51 44 


2 29 


218 


95 


— » 


8-8-9 


52 56 


I 52 


269 


94 


n — 


8-9—8 


49 47 


2 25 





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May 1877. Mr. Froctor, Approaching Oppoiitian of Mars. 425 



The Approaching Opposition of Mars. By B. A. Proctor, Esq. 

Want of leisnre has prevented me from preparing, as I had 
intended, a paper indicating the probable appearance of Mars, on 
different days, dnring his approaching opposition. Herr Marth's 
excellent Ephemeris in the last nnmbcr of the Notices in large 
degree subserves the purpose of antioipatoiy charts, such as I 
drew in March 1873 ; for it is easy from the data he supplies to 
make ortho«>nal projections for any given day and hour. 

My chiei object in writing now, however, is to express my 
agreement with Dr. Terby, of Louvain, as to the doubtful features 
of my chart. Indeed several of the doubts he suggests had been 
indicated by the use of dotted outlines in my map. I agree with 
him also in considering that M. Flammarion's course, in making all 
the corrections which Dr. Terby says rightly may have to be made, 
is too summaiy . In some respects, indeed, the corrected chart is 
certainly incorrect. Thus, it carries Nasmyth Inlet eastwards as 
a narrow strait to join Tycho Sea, which may or may not be right ; 
but a correction which will certainly have to be made in this part 
of the map is overlooked altogether. I refer to a bay running 
southwards from this strait into Dawes Continent. This is shown 
well in drawings by De la Ruq, Knobel, and Qreen. I find it 
is shown in several of the views given me by Dawes, though 
not in the best. I ought to have remembered that positive evi- 
dence for a dark marking is altogether stronger than negative 
evidence against it. For a similar reason, on the other hand, I 
think it unlikely that the J. Herschel Strait of my chart does 
not extend into De la Bue Ocean. For some of Dawes's best 
drawings, in making which he paid special attention to this 
region, show the strait continuous. See especially his drawing 
numbered 10 in vol. xxv. of our Notices. See also Mr. Knobel's 
excellent series of drawings in vol. xxxiii. This positive evidence 
seems conclusive. The marked gap in Lockycr's views (among 
the best we have) indicates that clouds had gathered over that 
region — where the strait is manifestly shallow, so that mid- 
day clouds would readily form, as over shallow seas on our own 
Earth. 

I have here used my own nomenclature, which was devised 
simply for convenience of reference. If Dr. Terby had altered 
the names, all or any, I should have adopted the names he used. 
But as he, who has given so much attention to the subject and 
studied so many drawings, has adopted my nomenclature, I have 
not thought it necessary to follow M. Flammarion (who employs 
Dr. Terby*s results and my own) in changing most of the names. 
The changes seem uncalled for and likely to introduce confusion. 

2 North Road, Clapham Park, S.W. 



424 Mr. Proctor, Note on Distribution of Fwcd Stars, xxxvil. 7, 



Note on the Coming Opposition of Mars. By N. E. Green, Esq. 

In order to utilise the Opposition of this interesting planet, 
and secure afiedr amount of uniformity in the drawings of various 
observers, special forms have been printed on a paper possessing 
peculiar &cilities for the production of effect. 

This paper consists of an under^urface of white enamel 
covered with a warm tone closely resembling the general tint of 
Mars. Upon this surface the dark marks may be drawn either 
with chalk or pencil, and softened with the stump in the usual 
manner. 

The peculiar advantage consists in the use of the knife, by 
which the most delicate alterations of tint or form may be 
effected, or the warm tone partially removed for faint lights, or. 
entirely erased for the polar snows. 

The only care required is to avoid the use of india-rubber, 
all general soflening or removal being effected by bread. 

Sheets of these forms may be obtained at the monthly meet- 
ine in June, or by letter to N. E. Green, 3 Circus Boad, St. 
John's Wood, who will feel much pleasure in supplying them to 
the Fellows. 



Note on the Distribution of the Fixed Stars. 
By R. A. Proctor, Esq. 

Von Littrow has shown that when only the numerical 
relations of stars of various orders of brightness are considered, 
the increase in the number of the fainter stars corresponds with 
the theory that apparent magnitude depends chiefly on distance. 
When, however, the localisation of stars of various orders is 
considered, we find evidence of the numerical superabundance of 
stars really smaller than their neighbours. To take a rough 
illustration of the effect of this consideration : If, in examining 
any telescopic field taken at random, we find for each increase of 
illuminating power an increasing number of stars, the inference 
is that we are penetrating further and further into space. But 
this inference must be rejected if we find that the field of view 
lies in either of the nubeculce, and that the increase is not recog- 
nised, or only occurs in a markedly less degree, outside the borders 
of the star-cloud. In like manner, though not so obviously to 
ordinary vision, we find evidence of the existence of clouds of 
stars or streams of stars (such as are found in various parts of 
the Milky Way) ; and numerical increase with increasing powers, 
if found within such clouds and in markedly less degree outside 
their borders, cannot be referred to increase of distance, but, 
according to the laws of probability, must be explained as due 
to the recognition of stars really smaller lying within the limits 



Mmj 1S77. Eev, S. J. JvhnsoUj Visible Transits of Mercanj etc, 425 

of sach dondfl or streams. (By streams I do not mean rows of 
stars, but stream-ahaped reg^iona in which are many thousands of 
stars.) I think my Cfhart of 324,000 Stars in the Northern Hemi- 
sphere demonstrates this, especially when it is remembered that 
mb regions where these stars (largely exceeding in number those 
dealt with statistically by Von Littrow, or indeed, so fiar as I 
know, by any other) chiefly congregate, are precisely the regions 
where stars down to the 20th magnitude are found in greatest 
number. As Mr. W. M. Christie remarks in a very able and 
impartial review of my researches {Academy for June 27, 1874), 
*'it is hardly conceivable that*' the clustering aggregations 
''should be enormously long cylinders or spindles, turned in 
every case exactly towards us." 

It appears to me that direct evidence based on the laws of 
local aggregation, as deduced from isographic charting (which is 
in effect statistical enumeration recorded so that all its classifi- 
cations can be see^i)^ cannot be disposed of by a less perfect method 
of counting, in which averages only are considered without 
reference to localisation. This would be much as though an 
archssologist's theory respecting certain mounds in a plain should 
be met by a surveyor with the argument that the mounds had no 
real existence, seeing that, if they were levelled, the plain would 
not rise appreciably, where they liad been, above the surrounding 
level. If the mounds could be thus disposed of, any theory 
respecting them would fall to the ground. In like manner, I 
must admit that if no attention be paid to the evidence of stellar 
aggregation in particular regions of the heavens, there remains 
little evidence of the existence of real stollar aggregations in 
space. 



Visible Transits of Mercury to the Year 2000. 
By Rev. S. J. Johnson. 

Upon recently making an examination, for curiosity, of the 
transits of Mercury that were to be expected in this land till the 
dose of the next century, I found the method of cycles, even 
that of 263 years, would not answer in many instances, as, owing 
to the difierence of the planet's geocentric latitude at the return 
of the period, the duration of the transit may vary considerably. 
I therefore computed the places of and $ from some approxi- 
mato tables — those given in Lindsay's Chrono- Astrolabe — and the 
results will, I believe, deviate little from the truth. 

Thirteen transits of Mercury fall in the present century, but 
one only, that of 1832, was visible throughout at Greenwich. 
In the next century twelve happen, four of them being entirely 
visible there. 

After the transit of 1878 there will be no opportunity for a 
good observation of this sort in the remaining years of this 



426 Extract from a LeWvr etc XZXVIT. 7, 

ocDinry, as in 1891 the planet leaves the Sun scarcely half an 
hoar after snnrise, and in 1894 the ingress is bnt a quarter 
of an hoar before snnset. 

Sometimes a period of thirty years elapses that is transitless 
so far as we are concerned in this country, as between the years 
1802 and 1832, and from 1973 to 2003. 

(Contacts bdov the horizon are omitted) 
1 88 1 Nov. 7 Below the horizon. 



I89I 


Xaj 10 


»> 


>t 


Egress 


abont 4}^ mom. 


1894 


Nov. 10 


Ingress 


abont 4^ aft. 








1907 


Nov. 12 


it 


„ loj* mom. 


» 




If* aft. 


I9I4 


Nov. 6 


ft 


„ 9}^ mom. 


tt 




2^ aft 


1924 


May 7 






tt 




5|^moni. 


1927 


Nov. 8 






it 




8^ mom. 


1937 


May 10 


it 


„ 8^ mom. 


») 




g{^ mom. 


1940 


Nov. 10 


Below the horizon. 








1953 


Nov. 13 


Ingress 


abont 31" aft. 








i960 


Nov, 6 


it 


„ 2P aft. 








1970 


May 9 






11 


w 


noon. 


1973 


Nov. 9 


ft 


„ 7 }•» mora. 


»i 


tt 


I* aft. 


1986 


Nov. 12 


Below horizon. 








1999 


JJov. 14 


Below horizon. 








Upton Helions Rectory, 
Crediton, 











Extract from a Lettei' received hy Mr, Ranyardfrom Prof. Meiicct 

of the Museo Reale, Florence. 

1 have recently found, in the collection of instruments under 
my care, an Arabian Celestial Globe, which I believe is certainly 
the oldest of the few in existence ; its date is 108 1 a.d. It is made 
of metal, and its diameter is 209 millimeters. It represents the 
celestial sphere as given by Ptolemy, except that the longitudes 
of all the stars are augmented by 14° 10', so that we find Eegulus 
at 16° 40' Si &C' The names of the constellations are all in 
cufic charactei*s. There is also an inscription in the same 
character to the effect that the globe was made by Ibrahim Ibn 
Saidal Sahli al Wazzon (the Weigher), with his sonMuhammed. 
The work, it appears, was finished in Valencia, in the beginning 
of the month Safar, in the year of tlie Hegira 474 (this month 
began July 11, a.d. 108 i), and it was made for Abu Isa 
Ibn Labbun (or Lebun). 







^M^ 



MONTHLY NOTICES 

OF THE 

ROYAL ASTRONOMICAL SOCIETY. 

Vol. XXXVII. June 8, 1877. No. 8. 

William Hugoins, Esq., F.R.S., President, in the Chair. 

Major- General John Baillie, 25 Hamilton Terrace, St. John's 

Wood; 
Thomas Brewin, Esq., 14 St. Nicholas Street, Leicester; 
G. Calver, Esq., Hill Honse, Widford, Chelmsford ; 
James Campbell, Esq., F.R.G.S., Arkley Honse, Bamet ; and 
W. F. Denning, Esq., Tyndale House, Ashley Down, Bristol ; 

were balloted for and duly elected Fellows of the Society. 

The Rev. T. Tordiffe and Mr. J. G^rbutt were expelled from 
the Society for non-payment of arrears of subscriptions. 



Note on some of M. Stephan's New NehtUce. 
By J. L. E. Dreyer, Esq. 

Among the new Nebulae, the positions of which were given 
by M. Stephan in the April No. of the Monthly Notices^ are 
a few which already have been found before. M. Stephan has 
himself suspected this in the case of No. 1 2 of the first list, as 
he says : " Le No. 12 est peut-etre identique avec 440 Lassell." 
This identity is, however, quite certain, as the Nebula in question 
has been found independently by D' Arrest, whose position, 
brought up to 1876, is 

2i»> 20" 9"'3 97° 32' 13" 

in perfect accordance with M. Stephan. 

With respect to Nos. i and 2 of the second list, a comparison 
with D* Arrest's observations will likewise show that these are 
identical with H. III. 441 and 442. D' Arrest (who has found 
near this place several new NebuleB which seem to have escaped 
M. Stephan) has the following positions for i860 : — 

1 1 



428 Pro/. Newcomb, On the new Inequalities xxxvii. 8, 

h m 8 o I M 

I 20 i8'9 92 38 49 

I 20 37*9 92 36 55 

while the places of M. Stephan are for i860 : — 

h m R o / // 

1 20 i8'8 92 38 17 

I 20 408 92 36 15 

The " General Catalogue " is therefore wrong with respect to 
these two Nebnla9, while Auwers finds positions which agree 
better with the modern determinations. 

Through the kindness of M. Stephan I have been able to 
insert these two lists of Nebulse in my supplement to the " Gene- 
ral Catalogue/* which was read before the Royal Irish Academy in 
February last, and which I hope will soon be in the handfs of 
astronomers. The numerous cases in which Marseilles nebuke 
had been discovered independently by D* Arrest or Marth, have 
shown that M. Stephan almost always estimates the nebulae &r 
fainter than the other observers of nebulad. The descriptions 
" eeF," " presque inobservable," <fec. should therefore not deter 
observers from looking for these objects. 

Earl of Rosse^s Observatory, 
June 1877. 



Note oil the new Liequalitle^ in the Mamies Longitude, pointed out 

by Mr. Neison. By S. Newcomb. 

The inequalities in the Moon's longitude pointed out by Mr. 
Neison in the April No. of the Monthly Notices, if real, are so 
important, that I may be permitted to express the desire to see 
his computations of them published in extenso. They are, 
properly speaking, inequalities of long period in the mean 
longitude and in the eccentricity and perigee of the Moon, pro- 
duced by the action of Jupiter, admitting of being expressed as 
follows : — 



// 



5/= +220 sin (2w — 2 J). 

e^w = +0*58 sin (2w — 2J), 

5«' = —0*58 cos(2w — 2J), 

« being the longitude of the ^Moon's perigee, and J the mean 
longitude of Jupiter. The value of the varying angle is 

o o 

2xr — 2J = 2S70+2065 (/— 18000), 
= 239-4+ 2065 (<— 18500). 

My present object is to show how strongly the reality of these 
inequalities is indicated by observations. In No. 3 of Papers 



June 1877. in the Moon's Longitude etc, 429 

pabtished by the Traimit of Venus Commission, pages 20-29, ^ 
difloossed an apparent inequality in the eccentricity and perigee 
of the Moon, having a period of abont i6§ years; an abstract 
of which discussion is given in the Monthly Notices for June, 1S76. 
The notation used was 

substituting c e and ecw for h' and k'j the inequality indicated 
was 



u 



He = 075 sin N, 
cJtr = 075 COS N, 

in which the value of N indicated by observations was 

N « i63°-2 + 2i°-6 (t- 1868-5) ; 

and therefore, putting 

N'= N + 90° = 253^2 + 2i''-6(^-i868i), 

the inequalities were equal to 

«8tr 5= —075 sin N', 
8tf = 075 cos N'. 

We have, then, for the comparison of the angle N' derived 
empirically &om observations, and the angle 29— 2 J of 
theory 

N'=i 253-2 + 21 -S (^-i868-i), 
2tr-2j = 261-4 + 2065 (^-i868-i). 

The correspondence is so close that the identity of the two 
arguments does not seem to admit of reasonable doubt. 

What is worthy of remark is, that the period of this argu- 
ment differs but little from that of the Moon's node, so that the 
inequalities in question may, for many years at a time, appear 
to depend on the position of the Moon's node. They will there- 
fore produce apparent inequalities like those containing the 
Moon's mean anomaly, and the longitude of its node, which have 
been deduced by the Astronomer Royal in the Memoirs of the 
Royal Asiroiwmical Society, vol. xxix., pp. 13-15. 

The inequality of mean longitude will account for the difference 
between the values of the inequality depending on the ellipticity 
of the Earth as found from theory and from observations. 
Hansen's theoretical value is 

7"-76 sin {151° + I9°*34 (i- 1800)}, 

while the Astronomer Royal found a co-efficient of 6"'44. Now, 
in 1800, the argument of Mr. Neison's inequality was i36°great<;r 
than that of Hansen. The excess increased from 71° in 1750 

112 



43^ Lord Lindsayy On the Spectra xxxvii. 8, 

to 20I® in 1850. The effect of the new inequality was, it will be 
seen, to diminish the apparent inequality due to the ellipticity of 
the Earth during the period 1 770-1850, the diminution being 
zero at the first epoch, and attaining its maximum of 2''* 2 
between 1840 and 1850. 

A more definite statement of the support which the observa- 
tions give to the inequality of longitude cannot be expressed 
without a more continuous compariison of Hansen's tables with 
observations than now exists. 



On the Spectra of Comets b and c, 1877. By Lord Lindsay. 

Already, on April 11, the spectrum of Winnecke's Comet, 
(b 1877) was seen to consist of three bright lines. Under a very 
low dispersive power these seemed to be connected by the very 
narrow continuous spectrum of the nucleus ; but on subsequently 
applying a higher power it was obvious that, although the lines 
were much widened when the image of the nucleus fell on the 
slit, still the spectrum was broken up into three lines separated 
by wide dark intervals. 

Measures were obtained with a Browning single prism spec- 
troscope, on April 18, by Gopeland and O. Lohse: the resulting 
wave-lengths in millionths of a millimeter are 

556*0 Very faint line. 

516*0 Bright line abruptly terminated on the side next the red, bat gradually 
fading away towards the violet. 

472*2 Faint line, somewhat sharply bounded towards the red. 

On May 5 the same instrument gave wave-lengths 5580, 
508*6, 467*9 ; the lines being much the same as before. 

The followinsr night was very clear, and by using a very low 
eye-piece the lines were found to be visible, even in a Grubb 
spectroscope with a large compound prism. The least re- 
frangible of the three lines was now found to be separated into 
at least three very faint lines, see figure, A series of measures 
gave the wave-lengths as follows : — 

5696 Very faint line. \ 

559*3 ) I 

[ Very faint band. V These form parts of one band. 

543*2 Very faint line. / 

517*5 ) 

^ \ Limits of brightest line. 
4986 ) 

513*4 Brightest part of brightest line. 

5 10*7 Centre of light of brightest line. 

470*5 Brightest part of faintest line. 



1 1877. of Comet* hande, 1877. 




432 I^. Oopelandy On two *^ Flats'* xxxvn. 8, 

The spectram of this comet much resembles that of Comet II. 
1868, as figured by Dr. Huggins in the PhU. Trcuns, 

The spectrum of Comet c was first successfally metsured on 
May 5 : it too consisted of three bright lines, but none of them 
coincide with those of the other comet. The results are 

m.m.m. 

467-6 Faintest line ; brightness ss 2. 

507*9 Brightest line ; „ ■■ $. 

528*2 „ „ »i " 3* 

The last line is very olose to E of the Solar Speotnun. 
There we have to deal with a comet closely allied to drorsen's 
Comet of 1868 and Comet L 187 1. 

The measures were all made with a spider's line, or a steel 
cone, in either case feebly Ulnminated in an otherwise perfectly 
dark field. The steel cone is probably the best, as it giyes a 
broader line and requires less illumination. 

Dtmecht Observatory ^ 
1877, May 8. 



On two ^^ Flats " on the Moon's Inmb, observed March 23, 1877. 

By Dr. Ralph Copeland. 
(Communicated by Lord Lindsay.) 

At ii*» 50™ G.M.T. on ]March 23, 1877, while preparing to ob- 
serve the reappearance of *: Oeminonim, I noticed two remarkable 
"flats" on the Moon's limb. The position angles of their centres 
were found to be 264° 28' and 272° 30' ; their lencrths being 1' 39*"i 
and i' 1 8*" 2 respectively. These depressions coincided sensibly 
with a spider's line through oat their entire length. Assuming the 
lowest points to have been exactly on the Moon's limb, the above 
measures give the following results : — 

Depressions of March 23, 1877. 

ist Depression. 2nd Depression. 

Length in arc of Moon's limb 5° 46' 4° 3'' 

Apparent depth i"-24 0^*78 

„ „ in toises 1125 703 

Selenocentric Latitude — 14® 25' — 6° 1' 

„ Longitude +87 18 +86 41 

For the sake of comparison, it may be mentioned that the height 
of Pico is 1,062 toises according to Beer and Miidler. 

It is highly probable that these indentations are identical 
with two of those seen by the Rev. H. Cooper Key on September 
6, 1863. The second of them was again seen by Mr. Birt on 
I^ovember 3 and 4, 1864, and still later on November 12, 1875. 



June 1877. on the Moon* 8 Limh, 433 

Bat the best observations I have been able to find are by Dr. 
Erck on November 11, 1875, ^^^ observed them with his 
Tiwinch Alvan Clarke (See Astronomical Register, No. 156). 
Bus words are : " On laying the thick bars of the micrometer 
parallel to them I found their position, inverted, to be respect- 
ively 153° and 146°. The largest of the two flats was at 153®, 
and for something more than 3 minutes of arc, corresponding to 
12^ of lunar latitude, the limb did not deviate from the straight 
edge of the bar." It is not quite clear what is meant by 
" inverted " positions, but supposing them to be counted irom 
the parallel — they were measured with the bars — the positions 
would become 243° and 236°, and would fall on the Moon's 
bright limb,* and the depressions would be identical with those 
observed at Dunecht, the results being : — 

Depressions of November 11, 1875. 





146° Depression. 


153** Depreaslon, 


Length in arc of Moon*s limb 




io«> 18' 


Apparent depth 




4"-05 


„ M in toises 




3599 


Selenocentric Latitude 


-14° 21' 


- 7° 2d 


„ Longitude 


+ 85 3 


' +84 16 



The depth is nearly equal to that of Newton, the deepest 
known crater in the Moon, the bottom of which is 3727 toises 
below the highest peak of the rim. 

Guided by the above results, there is no diflRculty in coming 
to the conclusions that — 

The ist of the depressions is most probably caused by the pre- 
sence of the adjoining ring-plains Ansgarius and Behaim on the 
^oon*s limb ; 

And that the 2nd depression is undoubtedly a vertical section 
of Kdstner, 

Schroeter, who first described the ring-plain Kaestner, Saw it 

on the terminator 20 hours after fall moon on February 23, 

1796. The grey surface of the plain then appeared to be entirely 

cjot off from the Moon by the shadows of the mountains on the 

eastern margin. On the occasion of its discovery (September 30, 

'792) Schroeter found the length from N. to S. to be 3'4o", a 

Measure fairly agreeing with Dr. Erck's " something more than 

3 minutes of arc." Beer and Madler have also seen the floor of 

-fCdstner separated from the rest of the Moon, but the Rev. 

Cooper Key seems to have been the first to notice its projection 

^ti the Moon's limb. 

Dunecht, June 7, 1877. 

* 153° an«) 146° are out of the question, as being on the dark limb ; but, 
^ortnnntely, Mr. BirtV general account of the appearance and position of the 
depressions on the following evening points positively to a part of the limb 
^ear Kdstncr. 



434 



Mr. Tehhutt, Occtdtations etc. 



xxxvn. 8, 































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JoDe 1877. Mr, Ellery^ Observations ofu Centauri, 



435 



ObservaHons of a Centauri. By R. L. J. Ellerj, Esq., F.R.S. 

As I lee in the Monthly Notices that Mr, Marth* has urged 
obfervations of a Centauri at the present time, I snbjoin the 
resnltB of oar observations of this Binary. 

From measures obtained in March and April 1877, the dis- 
tance of the components appears to be 3^*3 and the position 
69^*1. In 1862 the position was 0*0, and distance 10", since 
which time the position angle appears to have gradually in- 
croased, the distances obtained ranging from 10'' in 1862 down 
to 8" in 1874, with an indication of a maximum about 1868. 

The clpse proximity of the components at present, combined 
with their great brightness, render accurate measure of position 
a very difficult matter, and also, no doubt, interferes with very 
inrecise distance measures. Further measures shall be made, ana 
the results forwarded to the Society. 

The following are the only measures recorded at this Obser- 
vatory : — 





Dist. 
// 


Po«. 




18637s 


8-5 


S-a 


186472 


8-1 


• • • 


1868*17 


9*2 


• • • 


186818 


9-6 


• • • 


1870-65 


10*2 


• • • 


I873I6 


8-3 


■ • • 


I874I5 


80 


305 


1876-61 


45 


50-1 


1876*62 


3-8 


520 


1876-94 


4*5 


51*2 


1877-19 


33 ) 




1877*21 


34 




1877*28 


2-8 


) 691 


1877-28 


2-98 




1877*28 


316 





Each result is the mean of from 6 to 10 measures of distance, 
and from 2 to 10 of position. 

The table below gives the position and distance as deduced 
from our Transit Circle observations of a^ and a' Centauri, and 
although they can scarcely b^ taken as so accurate as the 
micrometer measures, they indicate the movement of the system 
with considerable precision. 



436 Mr, Flummer, On fhe Oolleciive Light xxxyti. 8, 

Angle of Position and Distance of a} Centauri with regard to a* Cenieutri, 

from Melbourne Transit Observations. 



Year. 
1862*47 


Dist. 

• ■ ■ 


P. 



Kg. of H< 
3 


1865-56 


995 



17-3 


I 


1868-51 


1 1 02 


21-8 


5 


1870-65 


10-45 


247 


3 


1871-51 


9-41 


24*2 


I 


1872-55 


10-36 


24-1 


I 


1875-94 


6-68 


393 


I 


1876-90 


4*94 


64-3 


I 


Melbourne Observatory ^ 
1877, April 17. 






% 



On tJie Oollective Light and DistrihtUion of the Fixed Stars, 

"By John J. Plummer, M.A. 

The object of the following paper is to determine within fair 
limits of approximation the total illnminating power of the 
stars as compared with some acknowledged photometric standard. 
In endeavouring to do this I have been led to certain considera- 
tions regarding the distribution of the stars in space which are 
not in accordance with the theory so ably enunciated by Mr. Stone 
in the March No. of the Monthly Notices, but point to a more 
complicated structure of the sidereal universe. Although readily 
obtainable from existing data, these remarks may not be the less 
interesting to the fellows of the Society, as I am not aware that 
they are to be found elsewhere. 

The numbers of the stars of each magnitude are now known 
with great accuracy for the northern hemisphere, from the careful 
analysis by Littrow of Argclauder's Survey of the Northern 
Heavens. Nothing more satisfactory could be desired as regards 
the enumeration of the stars. The photometric value of Arge- 
lander's scale of magnitudes has been investigated by Pogson. 
The light-ratio determined by this observer is 25 12, but it will 
be sufliciently approximate to assume the first decimal place only 
as accurate. Further, it does not seem possible to fix any 
inferior limit to tlie magnitude of the stars which contribute 
towards illuminating sensibly our Earth, because it is well known 
that those which individually are too faint to affect the retina of 
the eye, when congrcprated in sufficient numbers, become dis- 
tinctly visible as hazy light ; and it would appear that every star, 
however small or isolated, must aid in the general illumination 
of the heavens in proportion to its apparent lustre. 



Jmie 1877. and Disirihution of the Fixed Sta/n, 437 

The following table has been obtained by combining the two 
BonroeB of information already mentioned, and gives the number 
of sixth magnitude stars to which the total light of the stars 
of the several classes into which Littrow has divided the 
Durchmusterung are equal : — 

T i.»iM«» No. of Stars in Northern No. of Stan of 6th 

Clam, ^f™i;I5L Hemisphere by Littrow mag. to which 

Magnitudes. ^^j j^g^Under. they are equaL 

1 I 'O to 1*9 lO 646-6 

2 20 „ 29 37 9570 

3 30 » 3*9 130 '3449 

4 40 „ 49 312 12911 

5 50 " 5*9 'oo' 16569 

6 60 „ 69 4386 2904*0 

7 70 » 7*9 13823 36609 

8 80 „ 89 58095 61544 

9 90 » 9*5 237131 12069-3 

If we assume that one-half of the light in class 6 comes 
firom stars that are visible to the naked eye, we shall have the 
brighter stars equal to 7349, and the telescopic stars down to 
the 9'5 magnitude inclusive, equal to 23337 standard stars of 
the sixth magnitude, or that fully | of the light of a fine night is 
derived from stars individually invisible to the naked eye. Next, 
taking the light of Sirius equal to 324 stars of the sixth magnitude, 
it will be found that the total light of the whole of the stars of the 
Diirchmu8tei*ung is equal to 10*17 x Venus at maximum brilliancy, 

^ ^ 8T of the mean full moon. As these results must be 
786 

approximately true for any hemisphere of the heavens, it follows 
that (disregarding the light of the fainter telescopic stars, of 
whose numbers we have no estimate) the illuminating power of 
all the stars above the horizon at one time is not less than 
■gjiih. part of the illumination due to the full moon ; but it should 
be remarked that in this estimate no deduction has been made for 
the absorption of light in passing through the lower portions of 
our atmosphere. 

With reference to the stars fainter than those here consi- 
dered, a difficulty presents itself. If their numbers increase in 
the same ratio as obtains in those for which we have determined 
a light equivalent, it must be admitted that only a small portion 
of the stellar light has been here taken into account ; and it be- 
comes desirable to determine whether from some cause or other 
there does not exist a greater number of stars of the 9th and loth 
magnitudes than the usual theory of stellar distribution in space 
will account for. In dealing with large numbers of stars the 
most probable supposition is, that variations of real lustre will 
be equalised, and that an average equal distribution fairly repre- 



43^ Mr, Flwnmer^ On the GoUecHve Lights etc. xxzni. 8, 

sents the actual condition of things. This amounts to the 
assumption that distance is the sole cause of variation of mag- 
nitude, which, while manifestly untrue for a few stars, must be 
accepted as approximately accurate for large numbers. If, 
therefore, we select one of the classes in Littrow's analjsia as 
containing an average number of stars compared with the space 
included within the limits of distance which the light-ratio 
assigns, it is easy to determine the number of stars that each 
of the other classes should contain. I have calculated these 
numbers for each class, on the supposition that class 8 contains 
such an average density of the stellar stratum, whose limits are 
determined by the light-ratio previously used ; but, from what 
has already been said, no great accordance is to be looked for 
except where a large number of stars are concerned. 



am. 


True Ntunbers 
according to Littrow. 


Calculated 
Numbers. 


Badius of Sphere fonii< 
ing Exterior Limit 
of Distance (Dist. 

of 6th Mag. Star si). 


I 


lO 


5 


01 56 


2 


37 


15 


0247 


3 


130 


60 


0391 


4 


312 


238 


o*6i8 


5 


lOOI 


941 


0977 


6 


4386 


3718 


1*545 


7 


13823 


14697 


2*443 


8 


58095 


(58095) 


3863 


9 


237131 


99631 


5085 



An inspection of this table shows that the final class contains 
a much larger number of stars than can be accounted for in this 
manner, and further that the comparison would not have been 
materially altered had either of the four preceding classes been 
selected as of average density. The significance of this fact may 
perhaps be more strikingly shown thus. Within the limit 039 
the numbers of the stars exceed the average, but are too few to 
admit of our saying decisively that they do not conform to the 
law of density that prevails at greater distances. From 0*39 to 
3*86 one uniform law of stellar distribution prevails, while from 
3*86 to 5 08 more than twice that density of stars must be 
assumed to account for their greatly increased numbers. The 
use of the light-ratio found by Carrington is equally ineffective 
to explain the facts, and there appears to rae but two suppositions 
capable of doing so. Either the Bnrchmustennig of Argelander 
contains many stars (more than one-third of the entire number) 
which, though rated as 95 magnitude, are sensibly below it,* or 

* This is equivalent to assuming that tho liffht -ratio, which applies well to 
the whole of the earlier portions of the scale, fails completely towards the end, 
and it is a point which I have long had some intention of investigating.* At 
present it is but justice to the deserved reputation of Argelander to assume 
that his icale of magnitudes is as uniform at the end as elsewhere. 



June 1877. Trof, Zenger, On a new Solar Eye-piece. 439 

dae it mimt be assnmed that, at the average distance for stars of 
ttoB magnitude, a denser stratum actnallj exists, sacceeded pos- 
db^ by regions less froitfol beyond. Haying been led to the 
Ifttter condnsion in opposition to preconceived ideas, I cannot but 
tbiak that the enormously increased ratio with which the lumbers 
of the telescopic stars are multiplied is deserving of increased 
ixitereBt and continued discussion. 

Orw$U Bark Observatory. 



A new Solar Eye-piece. By Prof. Zenger. 

The Solar Eye-pieces for viewing the Sun by large telescopes 
"e devised for the purpose of getting rid of the obnoxious glare of 
^e solar radiation. Bj dark coloured glasses, absorbing fluids, re- 
jection from polished glass surfaces, with or without the aid of 
polarisation of light, it was possible to view the Sun. But all 
^bcse contrivances could not entirely satisfy the requirements of 
^ observations ; either there was a mucn diminished field, as 
the case in using Dawes's solar eye-piece, or there was a loss 
^^^ definition by the use of polarising eye-pieces, or by double or 
^^ple reflection from the plane surfaces. 

To obviate all these hindrances, I imagined a solar eye-piece 
P^x^sisting of a catadioptric lens, the last lens in the eye-piece 
^^^ing replaced by a hemispherical lens, with a carefully worked 
^l^toe surface, inclined 45° to a 

**^ optical axis of the tele- l\ ^llfcr^ 

J^Ofpe. By this replacement H (| 1 Q>/ 

^© field of view is scarcely V 

•?^cted at all, and the defi- 

?*'^on is unaltered, or even improved; for the hemispherical 

^^■Xb reflecting the solar rays into the eye at (0) works like a 

^f^^erical lens, and the curvature may be lessened in comparison 

'^^'tt a plano-convex lens in the ratio 

I : -7-, or nearly i : 024 « 25 : 6 - 4 7 : i. 
2 o 

^ There is an equilateral prism placed in optical contact with the 
^'^^me sur&ce of the hemispherical lens, and denoting by n the 
~ X of refraction of the lens, and by n' that of the prism, the 
ity of the reflected light by the plane surface ac will be 

TV* tan'(a-aO 
T* "taii«(a + o')* 

The central rays falling on the lens and emerging after re- 
tion, at the angle of 45°, by ac, will be greatly reduced in in- 
tensity if there is only a small difierence in the reflecting power 
^ the two media. 



440 



Tfof. Zengetf On a new Solar Eye-piece. xxxvii. 8, 



We get 



, sin a 
BID o = — — 
n 

n 



m\/2' 



if n = 1*53, and n' = 1*544, we have : — 





Bl 


U » B 


— — 7- — w /v/ 

I '544^/2 






«'= 


44° 28' 58"- 1. 




a 


-«'= 


O® 31' r-Q; 


log 


tan (0- 


■aO- 


79555421 


log 


tan (a + 0') = 

tan (a-o') 
tan (a i- 0') 


1 207301 41 




5*9125280 


2 log 


1*8250560-10, 




tan* (a- 




6*6843. 1 o-». 



Taking the light of the fall moon = io~^ of the solar intensity, 
we get 






= 6-6843. IO"«, 



or the intensity is diminished to 0*007 of the intensity of the 
full moon as viewed through the telescope. 

The diminution of light is sufficient to bear the whole aper- 
ture of my four-inch refractor, or of my 4^-incli Browning with 
reflector, not the slightest trace of heat rays being perceptible at 
0, in the reflected light from the plane at\ but the radiation at h 
is suflicient to crack the dark glass and melt it. 

It is even possible to leave the eye- pieces unaltered, and to 
place behind the last lens, as nearly in contact with it as 
possible, two equilateral reflecting prisms a /v/>'c, in optical contact 

with each other, the hypothe- 
nnses ac being in optical con- 
tact. Nearly the whole radia- 
tion of light and heat is con- 
ducted to hy only 7 X 10*^ of it 
being reflected to the eye at O. 
A dark chamber of black- 
ened brass plate is placed round the double prism to get rid of 
the dispersed light, leaving an opening near the eye. 



I 




June 1877. Lord Lindsay, Corrections to Struve^s Double Stars. 44 f 

Both dispositions show the San in a most surprising manner, 
free from any coloration, as an intensely white heJl, blnish at the 
middle, and rapidly decreasing in intensity, the borders being of 
a myish yellow tint. A 2^.inch Plosal Dialyse shows the same 
coTonr as the 4-incli refractor, thongh the secondary spectrum 
in the former is much more visible than in the larger telescope. 
I suppose this colour to be due to a diminished intensity of light, 
together with a yellowish ruddy colomtion of the borders by the 
absorption of light in the deeper layer of solar atmosphere 
through which the light passes. 

Prague, March 17, 1877. 



Oorrections to Struve^s Double Stars contained in tlie Dun Echt 
Observatory Publications^ Vol, L By Lord Lindsay. 

Mr. Bumham of Chicago, U. S. A., has most kindly sent me 
a list of errata and misprints which he has found in the first 
volume of my Observatory Publications, while reading it with 
the MS. of his own general Catalogue of Double Stars. As it 
may be of service to some of the Fellows, I venture to ask for its 
insertion in the Monthly Notices, 

Corrections. 

80 Colour For ash Read blue 

87 Mag. of A „ 8-5 ., 80. 

112 Decl. „ 45° 27' „ 45° 4''- 

300 Decl. „ 38^55' „ 28^55'. 

376 Position „ 35i°-22 ,, 25i°-22. 

444 Name „ v „ n. 

548 Distance „ i4i"-97 „ I4"'I97- 

563 Decl. „ 10^ 50' „ 40° 50'. 

544 Epoch „ 3072 „ 3172. 

635 Decl. „ SO^ $1' „ 54° 51'- 

733 I>ecl. „ 15^57' ,. 15° 52'. 

943 Position „ I55°'90 „ i65°-90. 

977 l>ecl. „ 48^45' M 48° 39'- 

983 CJolour „ yelsh. „ yel. 

990 Decl. „ - 14° 16' ,. - 14? 6'. 

1012 „ „ 38° 20' „ 28° 20'. 

1058 „ „ 9^3/ M 9° 47' (I'os. Med.) 

1062 The Decl. measures and Maguitudcs all belong to IS 1065. 

1066 Epoch „ 3972 „ 2972. 



44' OorreeHon to Mr. Douming^s Paper etc. xxxyn. 8, 



"S3 


DecL 


For 


12° 3/ Read 


I2*> 20'. 


1245 


Mag of A 


» 


8-6 


If 


60. 


1292 


Bed. 


It 


0^6' 


If 


-o<> 6'. 


1526 


tt 


If 


3° 22' 


fi 


3° 30'. 


1525 


»f 


II 


49^9' 


II 


48° 9'. 


1714 


1* 


If 


-24^19' 


11 


240 19'. 


1727 


Position 


If 


324«-97 


If 


334° 97'. 


1806 


Decl. 


»i 


39^7' 


II 


49° 7'. 


1928 


Position 


II 


2270-65' 


If 


277«-65. 


1949 


Decl. 


II 


13° 47' 


II 


13° 27'. 


2008 


f» 


II 


2O18' 


fi 


-2« 18'. 


2036 


i> 


If 


520 49' 


If 


72° 49'. 


2099 


»» 


If 


70° 23' 


If 


70° 35' (Pos. Med.). 


32» 


f> 


II 


47^42' 


ff 


47° 32'. 


3110 


n 


fi 


-2045' 


f f 


-2^25'. 


2499 


Position 


ff 


329'''43 


1 
fi 


324°-93. 


2589 


Distance 


ff 


5"o88 


If 


5"oo8. 


2601 


•Position 


fi 


I i6°o5 


ff 


i66°o5. 


6o« 


• 


11 


310° 


ff 


2IO^ 


3rook Street, 

June 6, 1877. 











Correction to Mr, Bowning^s Taper on the " Determination of the 
Semi-diameter of Veyius at the Mean Distance of the Sun from 
the Earth,^^ May No., pp. 398, 399. 

The Author writes that he has diocovered a slight inaccuracy 
in the computation of the Probable Errors on page 399. The 
corrections are : — 

For jr = 0'4439 ± 01036 xe 

read x= 0*4439 ± 0*1369 x<?; 

For y «= —002068 ± 000777 X e 

read y = — o*o2o68±ooii5i x c; 

For semi-diam. = 8*3693 ± 0*0664 x e 
read semi-diam. -i 8*3693 ± 0*0955 ^ ^' 



MONTHLY NOTICES 



OF THE 



ROYAL ASTRONOMICAL SOCIETY, 



Vol. XXXVIL Supplbmbntary Notice. No. 9. 



Leiier to the Hon. B, W. Thompson, Secretary of the Navy^ 
announcing the Discovery cf ScUelUtes of Mars. 

U.S. Natal Obsbbtatoby, WASHuroTOK, 
August 21, 1877. 

Sir»-*-Tlie oater satellite of Mars was first observed by Pro- 
fessor Asaph Hall, U.S.N., on the night of August 11, 1877. 
Cloudy weather prevented the certain recognition of its true 
character at that time. On August 16 it was again observed, 
and its motion was established by observation extending through 
an interval of two hours, during which the planet moved over 
thirty seconds of arc. 

The inner satellite was first observed on the night of August 
17, and was also discovered by Professor Hall. 

On Saturday, August 18, the discoveries were telegraphed to 
Alvan Clark & Sons, Cambridgeport, Mass., in order that if the 
weather should be cloudy at Washington, they might confirm 
the existence of the satellites with the 26.inch telescope of Mr. 
McCormick, which is in their hands. 

This discovery was confirmed by Professor Pickering and his 
assistants, at Cambridge, Mass., and by the Messrs. Clark, at 
Cambridgeport. 

On August 19, the discovery was communicated to the Smith- 
sonian Institution, by which it was announced to the American 
and European observatories in the following despatch : — 

Two satellite (f Mars discovered by Hally at Washington. First, 
elongation wekt^ August 18, eleven Iwurs, Washingto)i time, Dis^ 
lance, eighty seconds. Period, thirty hours. Distance of second, 
fifty seconds. 

It will be seen hereafter that the statement of fifty seconds as 
the distance of the inner one was erroneous. 

The observations hithertp made are as follow :•— 

K K 



444 



The SateUUes of Mars. 



xxxnL9, 



The First Saidlite. 








h m 




h m 


II 




ObMCiftf* 


877, Aug. II, 14 40, p= 59*6 


(2); 


H 45. 


8 » 70-57 


(a) 


HalL 


16, 1 1 42, . 




• 


. 8 » 77«6 


(0 


Hall. 


13 7, P- 71-9 


(2); 


• 


. » - 8083 


(4) 


Hall. 


13 36, . 




• 


. 8 « 80-4 


(0 


Hall. 


17, 16 2, |>= 85-5 


(2); 


16 19, 


8 « 6324 


(3) 


HalL 


18, 10 28, p = 2517 


(3); 


10 18, 


8 » 82-93 


(8) 


Nevcomb. 


10 57, p = 244-5 


(0; 


" 5. 


8 » 8i'6 


(I) 


Harkness. 


1 1 50, 2? = 246*6 


(4); 


II 57, 


«- 81-77 


(4) 


Hall. 


14 32, p =» 232*1 


(4); 


14 39. 


8 B 61*04 


(4) 


Hall. 


19, II 42, ^ = 2832 


(2); 


II 49, 


8 « 46*20 


(4) 


HalL 


15 43. i> = 255-4 


(4); 


15 52, 


« = 8i*37 


(6) 


HalL 


20, 10 28, p =s 6i*i 


(3); 


I0 33» 


8 = 76*07 


(a) 


HalL 


" 57. 1>= 521 


(4); 


12 7, 


« - 59*93 


(4) 


HaU. 


The Second Satellite. 








1877, Aug. 17, 16 6, i? = 73'0 


(2); 


16 21, 


8 « 30-81 


(4) 


HaU. 


18, II 31, p- 2488 


(2); 


II 37, 


« = 3465 


(4) 


HalL 


19, II 25, p ^ 2268 


(2); 


II 30. 


8 S3 2408 


(2) 


HaU. 


20, 13 15, p = 67-1 


(0; 


13 26, 


« - 31-95 


(3) 


HalL 


13 56, . 


• 


• 1 


, 8 = 2702 


(4) 


HalL 


14 22, p « 70 (est.) ; 


14 22, 


«= 1916 


(3) 


HalL 


16 19, p a 250 (< 


3St.); 


16 19, 


« = I515 


(7) 


Hall. 


16 35, . 


• 


• < 


, 8 = 16*70 


(7) 


Hall. 



From these observations Professor Newcomb has derived the 
following approximate circular elements of the orbits. The 
probable errors assigned are only very rough estimates. 



The OuUr Satellite. 

Major semi-axis of apparent orbit seen at distance [9*5930] . 82''*5 ± o"*5 

Minor semi-axis of apparent orbit seen at distance [9*5930] , 27"*7 ± 2". 

Major semi-axis of orbit seen at distance nnity . . , 32"-3 

Position-anglcsof apsides of apparent orllit .... 70°, 250*^*2® 
Passage throngh the west apsis (p = 250^), Aug. 19, i6*"6, W.M.T. 

Period of revolution 30*' 14™ ± 2" 

Hourly motion in Areocentric longitude . . . . 1 1°*907 

Inclination of true orbit to the ecliptic 25°'4 ± 2 

Longitude of ascending node 82^*8 ± 3 



Supp, 1877. Mr. OlatsJier^ On Solution of Kepler's Prohlem. 445 

Position of pole of orbit in celestial sphere . Long. 352*8 

Lat. + 64*6 
B.A. 316*1 
Bed. + 53*8 

These elements give for the Mass of Mars . 



3,090,000 

The Inner SatellUe, 
Ufajor semi-axis of apparent orbit at distance [9'593o] . 33^*0 ±1*' 

IPeriod of revolution 7** 38'»*5 ± o"*5 

Sonrlj motion in Areocentric longitude .... 47°' ii 
f^ssage through the eastern apsis (p * 70^ Aug. 20, 13^*0, W.M.T. 

Very respectfully, your obedient servant, 

John Bodqebs, 
Bear Admiral and Superintendent. 
The Hon. B. W. Thompson, Secretary of the Navy. 



On the Solution of Kepler^e Prohlem, 
By J. W. L. Glaisher, M.A., F.B.S. 

§ I. Writing Kepler's equation in the form 

X »a + etdnXf • 1 (i) 

the solution in powers of e is 

e* d e' cP 

X «a + eBina + — - 3r(8in«a) + --— -r-iCsin' a) + &c., 

1,2 da^ ' 1.2.3 cw' ^ 

and, on performing the differentiations, it will be found that 

X ^ a 

+ e.Bin a 
•fe^.sin a cos a 

•f c'.sin ocos'a— - sin* a 

2 

+ e^.sin o cos* a— ^~ sin* a cos a 

3 

II 1^ . 

+ e*.8in « cos* a— — sin* a cos' a + ~ sin* a 

3 ^ 

+ e*.sin a cos* a sin' a cos* a+ 7? sin* a cos a 

3 '5 

+ e'.fim a cos* «— ;5 «in* « cos* a + -Y^ sin* a cos* a- »^ sin* a 

+ e*.sin a cos* 0-^ sin* d cos* «+ ^ sin* a cos* a-^^ sin* a cos a 

3 ^5 3*5 

^&c» (2) 

K K 2 



446 Mr. J. W. L. Oladsher^ On the xxxvn. 9» 

Tbns, as is well knowo, the expression 

e sin a ,^^ 

a + (3) 

differs from the root of the equation (i) only by quantities of 
the order e^. It is also to be noticed that the second term of 
(3) represents the snm of the terms contained in the first column 
of (2), continued to infinity. 

It is evident, therefore, that if the value of the series (2) 
had to be calculated up to the terms of the fourth or a higher order, 
it would be preferable to calculate the value of the second term 
in (3) rather than the values of the terms in the first colunm 
of (2), so that, in the calculation of the terms in the other 
columns, we may assume that the value of log (i— 6 cos a) has 
been already obtained ; and it is of some interest to examine 
whether these terms can be arranged in such a manner that the 
knowledge of the value of log (1—0 cos a) may be applied to 
reduce the number of logarithmic entries required for their 
calculation. 

§ 2. It is clear that the terms in e^ and e^ in the second 
column of (2) can be represented by 



I c* gin' a 

SO that 



/» / viol 

2 (I -c COS a)» 



e? sin a I f' bin' a , , 

a+ (4) 

I -C cos ft 2 (i-cCOKrt)'''' 

differs from the root of (i) only by quantities of the order c'* 
in fact WO find that 

e sin a I r^ sin' a 
X =s a + 



i-tfcosa 2(i_ecosrt)> 

+ <?*.— o sin' a cos' a 4- sin* <7 

18 24 

+ c*. — o sm" a cos' a + ■ sin* a cos a 
81 15 

» 325 . • . 1291 . . , C41 . , 

+ £'. — ^'^'^ Sin' a cos* a + — - sin' a cos* a — - - sin' a 

162 120 720 

I ^039 • 1 i 427 . . , 1957 . , 

+ e". — "T^ ^^^ ^ COS a + ■ sin* a cos' a — -^^^ sm' a cos a 
729 15 315 

+ &^- (5) 



Bujip, 1877. Sohdion of Kepler*8 Problem. 447 

§ 3. The terms involving c* and e* in (5) 

- «•. — otan^a + ^ sin* a 
lo 72 

20 1^60 

+ e*. — ^ Bin* a cos a + -^ sin* a cos a, 
81 405 ^ 

e «^.— -o(^+ « cos a) sin* a 

lo ^ 9 ' 

. 43 , 10952 - . . 

+ «*. ^- (i + '-^ecosa)sin»a: 
72' 1935 

80 that these terms may be represented by 

i^ g* sin* g 43 e* sin* a 

l8(i-eco8a)V"^72(i-ecosa)VW* • • • (^) 

If the exponent — 25_ bo replaced by -^, the first two terms of 
the expanded value are 

^ «* sin* a (i + ■ ^ e cos a), 
72 '^ 1935 ' 

which differs from the quantity to be represented by only 



— ^ «• sin* a cos a B — «• sin* a cos a, nearly. 
3240 249 * -^ 

Thus the expression 

fl + A, 

where 

Atf sin a I c* sin* a i c^ sin* a 43 r* sin* a , , 

I -c cos a 2 (I -<r cos fl)V 18 (j _<; cos fl)V 72 (i -^ cos a)V ^'^ 

differs from the root of the equation (i) by 

— '^ t* sin* a cos a + terms of the seventh and higher orders, 
3240 

80 that practically (7) gives the solution of Kepler's problem to 
the sixth order inclusive. 

§ 4. Supposing the values of log e, log sin a, and log cos a 
to be given (in addition, of course, to the logarithms of the 
coefficients, which are assumed to be known), the calculation 
from (2) as it stands, up to the sixth order inclusive, would 
require twelve entries of the table of logarithms, while the 
calculation of log ( i — e cos a) requires two entries, and that of 
the terms in A four more, so that by the use of A six entries are 
saved. K log ( i — e cos a) be calculated and used in obtaining 
the first column of (2), the other terms in (2) require six entries, 
making nine in all, so that three are saved by the use of the last 
three terms of A. The calculatiou, of the expression (4), which 



443 Mr. J, W. L. Olaiaher^ On the zxxvn. 9, 

gives the valae of the root up to the foarth order inclasive, 
requires four entries, while the calculation from (2) requires six 
entries if the values of the separate terms in the first column are 
obtained, and five entries if they are replaced by 

sin a 



I — acosa 



§ 5. On developing the expression A up to the seventh order, 
it is found to be 

n e .sin a 
+ 0'.sinaco6 a 

+ c*. sin a cos* a— — sin* a 

2 

+ e*.sin a cos* a— -^ sin* a cos a 

3 

+ ff».8in a cos* a— -| sin* a cos* a 5 sin* a + z^ sin* a 

lo lo 12 

+ c*.sin a cos* a— *5— sin* a cos* a— 3- sin* a cos a+ ^-^ sin* a cos a 

oi oi 210 

+ e'.sin a cos* a— ^^^ sin* a cos* a— ^^ sin* a cos* a + ^-^ sin* a cos* a 

243 729 324 

+ &C, 



e .sin a 
+ e*.8in a cos a 

+ e*.8in a cos* a— - sin* a 

2 

+ e\sin a cos' a— -- sin* a cos a 



+ e^.Hm a cob* a— frm'rtcos^a+ -^ 



24 



sin* a 



+ 6*.fcin a o* a— - - sm' a cos' a+ ^ » sin* a cos a 

3 648 

, • « 7900 • .. 1 30935 • 

+ r. si.i a cob* « — - — bin' a cos* a + ^^ — ^ sin-' a cos' a 

729 2916 

+ &C. 

Subtracting this from (2), it appears that the correction to be 
added to A to give the true valine of the root of the equation ( i ) 
is 

c*. — — ^^ sin* a COS a 
3240 

+ e\ -4^ sin* a cos* « + -^/ sin* a cos- a - ^ sin' a 
1458 29160 720 

+ &C., 



Bapp. '1877. SohUion of Kepler's Problem. 449 

whioh very nearly 

— e*. am* a cos a 

249 

+e'. -^ — tin* a cos' a + :;3: siji* * cm' «— sin' « 
292 20 ^^ 4 

+ &C., (8) 

The BmallnesB of the coefficients of the terms of the seventh 
order in (8) compared with those in (2^ is worthy of remark : 
the snm of the first three coefficients in the e^ line in (2) is 
equal to about 23 and in (8) to less than nnity. 
It is noticeable also how nearly the expression 

I «■ sin* a 



2 (i— «cofl a)^ 



represents the first three terms of the second coltmm of (2), the 
coefficient of the third term differing firom — by only —. The 

quantity to be added to the expression in (4) to give the valno 
of the root up to the fifth order indnsive is 

«», — 5 Bin* fl + 3^ sin* a, 
which 



«•. — g sin* a + -^ sin* a, nearly,] 



Since 



5~ 72 360* 

§6. The numbers within square brackets denoting the Briggian 
logarithms of the coefficients expressed in seconds, the value of 
Ais 

r^ _ e sin a r^ ^ T e* sin* a r in ** ^^^^ ^ 

[5-3144251] , .cos a -[5-0133951],- ns- [4-0591526] 

I— c cos a (i— «C06o)» (I— ccosrt)» 

r- -c T ^ sin* * 

+ [5-090561 1] -r^. 

As an example of the application of this formula, let a = - 

4 
and e = 50°, this being the example considered on pp. 376, 377 

of this volume. 

The work is then as follows, every figure that has to be written 

down being printed : — 



< 



4SO 



Mr. J. W. L. Olaisher, On {he 



9t 



log* = 


9*3979400 log cos » 9*8080675 


M «• = 


8*1938200 


„ sin a B 98842540 


„ «»" 


1 6*9897000 


„ sin* a B 9*6527620 
„ sin* a » 9*4212700 


log e 9*39794a> 






„ coaa 98080675 






9*2060075 






e cos a 0*1606969 




] 


I -e cos a 0-8393031 




log (I 


-6 cos a) 9*9239189 






Ar. Co. 0*0760811 


- log P, say, 




0008453456 


-logPi 




0*25360368 


= logPV = logPV 




0*33813824 


= logPV 




0*42267280 


= logPV 




0-43112626 


= logPV = logPV 


( + ) 


(-) 


(-) (•^) 


5-3144251 


5013395 1 


4*05915 509056 


9-3979400 


8*1938200 


6*98970 6*98970 


98842540 


9*6527620 


965276 9-42127 


0-0760811 


0*2536037 


0-33814 0-43113 


4-6727002 


3-1 135808 


1*03975 1-93266 


47065-23 


1298-91 


10-96 85-64 


85-64 


10-96 




47150-87 


130987 




1309-87 







45841-00 = 12° 44' i"oo; 
thus A = 12° 44' I "'00, and 

ar = a + A, =62° 44' i^oo, (9) 

the true value being (see p. 377) 62** 43' 56"*oo. 

The value of the expression in (4), that is of a + the first two 
terms of A,= 62° 42' 46", and the correction for terms of the fifth 
order, viz. : 

I '1 

e^. — s sin* a + - sin* a 
18 5 

= -S"*'53 + 3i"*88, giving x = 62° 43' 13", 



Sspp. 1877. BchOion cf Kepler's Problem. 451 

§7. The oorreoiion to be applied to (7) in order to include 
qaproziinaUy the temui of the aeyenth order, viz.: 

«'.-^ sin* a — ^ sin' a 
20 10 

B o"-5o— i"'JS^ "" i"'2S« -Aj the error of (9) is abont 5", it will 
be seen that, tiie seventh order correction jnst obtained being 
very smally there is very little advantage in inclading these 
terms. In general, the classification of me terms according to 
orders of e supposes that e is very small ; so small, in fact, that 
a tenn involving e^' may be regarded as distinctly smaller than 

one involving e" : but if e be as large as -, the terms of the orders 

4 
near to 6^ do not differ much from one another in magnitude, in 

oonsequenoe of the increased values of the coefficients, which 

somewhat counteract the effect of the additional factor e. This 

is readily seen by considering the terms in e^. By expanding 

the tenns in A, it will be found that the terms in 6^, omitting 

the first} are 

m — 14*90809 sin* a cos* a— 1*44389 sin* a cos* a + 28*82887 sin* a cos* a 
V —16*35 198 sin* a 000* a <!- 27*38498 rin* a cos* a (10) 

(in whidh the coefficients are expressed as decimals so that their 
magnitudes may be more evident) : the terms in 6^ in (2), 
omitting the first, are 

■• -^ 16*33333 sin* a cos* a + 28*46667 sin^ a cos* 0^6*21270 sin' a cos a 

.... (u) 

and the difference 

B «*. 0*01865 sin* a 00s* a + 1*08169 sin* a cos* a-- 6*21270 sin' a cos a : 

in the case of e = -, this difference = o"*oo + o"*24- 1''*95 

4 
= -i"-7i. 

The close agreement between the coefficients of sin^ a cos* a 
and sin* a cos* a in (10) and (11) is remarkable ; and it will 
be noted that the coefficient of the new term, viz. the term in 
sin^ a cos a, is, as in the case of the terms of the seventh order, 
much the largest. 

It thus appears that if e be so large that, in order to obtain 
the value of a; to the nearest tenth or hundredth of a second, 
terms of a higher order than the sixth have to be included, in 
general no great additional accuracy will be obtained by applying 
to A the corrections for the terms of the seventh and eighth 
orders, while of course if the terms in e' may be neglected, the 
corrections are insensible. Whenever, therefore, the series in (2) 
affords a suitable solution of the problem, the expression a+A 
gives the solution up to the seventh order, and in general but 
utile additional accuracy is gained by applying the corrections 



452 Mr. J, W, L. Olaisher^ On the xxxvn. 9, 

for the seventh and higher orders. The advantage of nsing the 
formnla a+A wotild be greatest if e were very small, so that 
the order of c governed the magnitude of each term, and if the 
value of X were required with great exactness ; as, for example, 
if the accuracy required were such that ten-figure logarithms 
had to be employed in the calculation of the first term of A, bat 
that terms above e^ were insensible. 

The following are the values of the terms in (2), for this case 

of = -, a == 50°, up to the sixth order inclusive :— 
4 

+ 6347"-85 

+ I02o"o8— 724"'40 

+ i63"-92-388"-03 
+ 26"-34- 137"- 18 + 28*^78 
+ 4'''23- 40^-08+ 26"76 
= 5o«> + 4583o"-27 = 62° 43' 5o"-27; 
the terms in e^ 

= + o"-68 - io^''47 + 14"76 - i"'^e 

and the terms in e^ 

= o"-ii- 2"-54+ 6"-28-i''-9S 
« i"*9o; 

so that, when the seventh order terms are included, the value is 
62** 43' 53'' 7 8 ; and when the terms of the eighth order are 
also included, 62° 43' 55''*68. 

§ 8. As another example, let e = — , a = 50**, and the terms 

10 

of A 

- i6886"-23-57"-8s-o"-o7 + o"-47, 

so that a 4- A = 54° 40' 28^78, which will be found to satisfy 
the equation to within the hundredth of a second. 

§ 9. The exponents in the ' denominators of the terms in 

A are ^, ^, 5_ . if the last exponent be taken to be 5_ the 

9 9 9 9 

sixth order error 

» + -7 — «• sm* a cos a, = + — - c* sin* a cos a, nearly, 

and is thus much larger than when the exponent is ^, the error 
in this case {see § 3) being 

= — — c* sin* a cos a, nearly. 
249 ^ 



Supp. i877* Solution of Kepler^ 8 Prohlem. 453 

§ 10. If the terms in (2) be treated in columns as in §§ 2 
and 3, eaoH colomn being kept distinct, it will be found that 
up to the sixth order inclusive, 

sin a i_ g* sin* a _i_ g* sin* a cos' a 13 g* sin* a 
*°*'*'i-gcoso'"2(i»gcosfl)V'"i8 (i-gcosa)V'**24(i-.eco8a)W' 

so that 

X s: a + B, 

where 

_ g sin a I g* sin* a I g» sin* a cos' a 13 g* sin* a 



i-gcosa 2(i«<jco8a)V 18 (i-.cco8a)V 24(i«ccoBa)V' 
the correction to be added to B being 

g*.-^ sin* a cos a 

+ g\-*:s sin* a cos* a + -^^ sin* a cos* fl— t^ sin' a 
1458 3840 720 

+ &c., 
which, very nearly, 

a g>. — Sin* a COS a 
53 

+ g'. — sin* a COS* a + - sin* a— sin' a 
292 4 

+ &C. 

It is clear that the enression B is not so convenient for calcu- 
lation as A ; and also the residual sixth order term is larger for 
B than for A. 

§ II. In t. V. (1859) of the Annales de V Ohaervataire de Pa/ris, 
pp. 349, 350,* M. Serret gives an account of a method, indicated 
by M. Leverrier on p. 192 of t. i., of solving Kepler's problem 
by means of a series of a different form to (2). The method is 
as follows : — 

Let Xf, be an approximate value of x, and put 

V =3 a— Xo + gsinXo; 
then 

x—e sin x ^ Xq^c sin Xq-^v, 

This is the equation to be solved, and we can calculate x by 

* " Note sor T^nation dont depend Tanomalie ezcentrique, et snr les s^es 
qui 86 pn^entent dems la th^rie du mouyement elliptique des corps celestes.** 



454 ^^' J* ^' ^* Olaisher^ On the xxxm. 9, 

developing it in ascending powers of 1; by Maclaurin's theorem ; 
we have 

(i-.dcosar)^-i, 
(i-.cos*)^+ «8in*(^^j-o, 

When t; = o, oj t= aJo, and 





dx 
dv 


I cPar e sin Xo 




I— ccosjpo ^t'* (i-«coe*o)' 






d*x ^e^ sin* Xo e cos *o 
rf»" ^ (I — tf cos Xo)* (I — « cos Xo)* * 


whence 






X = «o + I— 


I 


^ I eeinxo ^, 

■» ^ /- y^^ 



+ 



/I r» 8in« Xq I gcosJo \^ , ^.^ /,,x 

l2(l-CCOSXo)* 6(l-<JCOSXo)*/'^'*"®*' ^"^ 



In the case of an orbit in which e is very small, pnt x^ = a, then 
v = 6 sin a and, neglecting terms of the fonrth order, 

<! sin fl I / r sin fl V # v 

jps=a + ( 1. .... (13) 

I— <;cosa 2 M—ffcosa/ ^ ^ 

M. Serrot remarks that this formula is very convenient for 
calculation, and that the last term can be immediately derived 
from the previous term. 

§ 12. It will be found that the coefficient of v^ in (12) is 

5 e* sin' Xo ^ e^ sin x^ cos Xo e sin x^ 

^8 (i — c COS jy)' 12 ( I — c cos j-y)<' (I— c cos j-y)*' 

and therefore, putting v^ = or, the formula, whose first three 
terms are given by M. Serret's equation (13), is 

f sin rt I i^ sin* a 



+ 



I— ccostf 2 (l— rcosfl)* 

1 r* sin* a l e^ sin' a cos a 

2 (I — c cos a)* 6 (I — c cos a/ ' 

5 f'' sin' a 5 r* sin* a cos air* sin* a 

— -^ - - + h 

8(1— c cos a/ 12 (I— c cos a)** 24 (i — d- cos «)•» 

+ v^'c. ; (14 

tie second line being derived from the terms in v^, and the third 
from those in v^. 



Snpp. i877- SohMon of Kepler^s Pfohhrn. 455 

In the case of e = -, a = 50^/ibis gives 

4 

X « 5o° + 47o65"-23— 1225"'24 
+ 63"79— 78^-20 



4''-i5 + 


9'»i6 + 5"-32 


+ &C. 




/ 


// 


The first line » 52 43 


5999 


the second line «> — 


14-41 


the third line => + 


1033 


52 43 


55-91 



The close approximation afforded by the first line (the error 
is only 3"'99) is very remarkable, but it is of course accidental ; 
the term of the fourth order = 7 8'' '20, and those of the fifth 
order amount to 69"'ii. 

§ 13. The formula (13), which is true to the third order, only 
differs from (4), which is true to the fourth order, in the 

exponent of the denominator, which is — instead of 3. If 

e = — , a = 50**, the last term of (13) = 56"*59 ; and the value 

of X from (13) is 54*^ 40' 29"*64, and from (4) is 54® 40' 28"*38, 
the true value as found in § 8 being 54® 40' 28"'78. 

As another example, let e = -, a being, as before, 50^, then 

7 
(14) gives 

* = 50® + 248S4"-92- i8o"-45 

+ 2"-62- 6"o8 

- 0"0S + 0''-22 + o''-22 

+ &C.; 

the first line = 56® 51' i4''*47, the second — 3"'46, and the third 
o"'39» leading to a; = 56° 51' ii"'4o ; and the true value obtained 
by substituting this in (i) is 56® 51' ii''*39. 
The value of a + A is 

50° + 24854"-92 - 1 86"-34 - o"-47 + 3"-34, 

which = 56° 51' 1 1 '''45. 

The value obtained from (4) is 56® 51' 8"*58. 

§ 14. It will be noticed that in both these examples the 
formula (13) affords a very close approximation to the true 
value; this is duo to the fact that the terms in the second 
line of (14) nearly counteract one another for the values of 
c and a that have been taken; for, these terms 

1 c* sin* rt r • 9 ' 1 
•» 1 n ^ [* 8IQ a -- cos rt}, 

2 (I -coos a)** 3 * 



45^ -^tf^' J' W. L. Cfladsher, On the xxxvil 9, 

and the term in brackets is email for the assumed values of 
e and a. As an example in which this is not the case, let 

e = -, a = 130°, then (14) gives 
4 

130® + 34032"*99-463"*25 

+ i2"-6i+ 2 1 "•38 

— o"-43— i"-46+i"*05. 

The first line =139° 19' 29"'74, the second 33"*99, and the 
third — o"'84, leadine to a:= 139® 20' 2"*89. 
The value of a+A 

= i30^ + 34032"-99-44o"-8i-2"-S9+ i3"-64 
«= 139° 20' 3"-23. 

The value of x given by (4) is 139° 19' 5 2"' 18, which only 
differs fix)m the true result (viz. 139® 20' 2"'93) by about 11". 
It is evident that the effect of the denominators in (7) and (14) 
is to increase the magnitudes of the terms if a be in the first or 
fourth quadrants, and diminish them if a be in the second or 
third quadrants. 

The expression in (4) is only very slightly more complicated 
than (13), and as it represents the root to one order higher, it is 
in general to be preferred. 

§ 15. The series in (14) is clearly the expansion of x in.powers 

of , and it may therefore be obtained directly in the 

I — e cos a 

following manner : — 
Let 



€ s= 



i—e cos a 
then 



. . 



I + c cos a * 

the equation is 

€ 

X = a+ sm X. 

I + € COS a 

viz. 

T ss a + € (sin x—x cos a + a cos «), 

and therefore, by Lagrange's theorem, 
ff=a+€Sina+ — ;t- (sm or— « cos a + a cos g)^ 

1 .2 QX 



— —^2 (sin ar—ar COS a + rt COB a)* + &c., . • . (15) 

.1 



Snpp. 1877. BohtHon ofKepler*8 Problem, 



457 



z being put eqnal to a after the differentiations have been per- 
fonned; thus 



9 m 



+ c • sm a 

+ €*. — an' a 
2 

+ €*. — 2"8in* a cos fl * 

+ &C 

It is evident that there will be no terms in the expansion in- 
volving powers of a cos a, for 

Bin X— X cos a + a coe a = sin a, when x =s a, 

and its differential coefficient =cos a;— cos a. When x = a this 
vanishes, and the terms are in conseqnenco greatly simplified : 
in fact, the development of (15) mav bo very rapidly effected. 
§ 16. A similar method affords the expansion of x in powers 

of ; for, let 

i+e cos a 



V- -. 



i+e COS a 



then 



X « a + 



smx, 



VIZ. 



and therefore 

« a a + 1} sin a + 



I— 71 cos a 
X ss a + ri (sin x + x cos a—a cos a), 

n^ d 



T- (sin x + ar cos fl— a cos a)' 
1.2 dx ^ * 



r^ d* . , \m o 

+ — ^ — T-i (sin * + « cosa— a cosar + &c., 
1.2.3 dx^ 



X being put eqnal to a. 
We thus find 



+ 1} • sin a 

+ 1;*. 2 sin a cos a 

+ !;•. 4 sin a cos' a— ^ sin" a 

+ i><. 8 sin a cos* a — ;^ sin* a cos a 

o 



f- 



+ ij». 16 sin a cos* a—-- sin* a cos* a + - - sin* a 

3 24 

+ &C. 



458 Mr. Oladsher^ On Bohdum of KeffUff% Problem. X1Z?IL 9^ 
The first colnmn OTidently 



fl Bina esma 



§ 17. I here add another solntion of Kepler's problem in 
series, the denominators of the terms being powers of i — cos a. 

If 

theU) by Lagrange's theorem, 

For = Fa + f/aFa + — :^ /»aFa + 5-^/»aFa + &c. 

•^ 1.2 da' 1.2.3 da* 

Now let 

- I dx 

i—ef'x da 
therefore 

dx_ I ^/af'a J^ d paf'a e* j« fafa . 

da i-(j/'a'*"(i-c/a)-'**i.2da(i-4/'a)»"*"i.2.3da«(l-«/a)»'*' 

efa e^fqf'a ^ d paf'a ^ 
--14. '' 4, ■'^' 4. — - - * •^ 4. jfe/» . 

^ \--cfa^ {i-^efaf^ \.z da {l^ef'aY^^^' ' 
whence, integrating, 

■*■ I -c/a "^ 1.2 (I -^j/'a)" ■*■ 1.2.3 da (i -if/'a)« "^ ®^ 
In the case of Kepler's problem 

fa a sin a, /'a = cos a, f"a « — sin a ; 
and therefore 

csina c* sin* a ^* d sin* a 

X n a -I — — — — — 

I— e cos a 1.2 (I— c cos a)-* 1. 2.3 da (i —c cos a/ 

i^ d^ fiin* a 



1.2.3.4 da"' (i — c cos ay 
e sin a 
l—e cos a 



e* sin* a 



2 (I — e cos rt)" 

c* f sin' a cos a /• sin* a 

3 I (i — f cos «)■- (i— ccosa)')* 

r* f wn' rt sin* a e sin* a cos a ^ f' sin' a ) 

— -I 20 — «— 2^ 22 — +6 ^4 

24 1 (I — fc'cosrt)^ ■'(i-ccosa)* (i-ecosff)* (i— «cosa)*J 



-&c. 

1877, August 4. 



Snpp. 1877. Mr. E, A. Proctor^ Note on the Arc of Light etc, 459 

Note on tJie Arc of Light seen rowvl Venus in Transit, 

Bj R. A. Proctor, Esq. 

My attention lias been directed to remarks made on this 
sabject after the reading of a paper by Mr. Brett relating to 
Venus, The paper itself I need not refer to. Bat the remarks 
upon it have raised hopes in some minds that it may be possible 
to increase the intrinsic brightness of light from a aisk or other 
yisible surface (as distinguished from bodies like the stars, 
which are reduced appreciably to points by distance). For it was 
assumed, in the first place, that the arc of light seen round 
Venus in transit (whether she is partly or wholly immersed) is 
really brighter than the Sun's disk ; and it was maintained in 
the second place, that this superior brightness could be accounted 
for either by the effects of a refractive atmosphere, or by 
specular reflexion at the surface of Venus, If this were so, it 
would be easy to produce the same effect artificially. The faint 
light of planetary disks, of nebulae, of comets, etc., might be 
strengthened, and at the same time rendered more suitable for 
direct spectroscopic observation, by interposing something of 
the nature of a large thermometer bulb — any opaque globe in fact, 
within a transparent envelope of suitable refractive qualities. 
This would be an important gain. Unfortunately there is no 
reason for hoping that it can ever be attained. The apparently 
superior brightness of the arc of light seen round Venus, or 
round a thermometer bulb held before a gas flame, or the like, 
is demonstrably due to two causes, neither implying any 
real accession of brightness, viz. — first, the effect of contrast 
against the dark disk within the refracting envelope, secondly 
and chiefly to the fact that the comparison is made between the 
light of some less brilliant part of the disk or other surface, and 
light from the whole disk or surface brought into view by 
refraction. It will be found on carefal trial, if the 'effect of 
contrast be. removed or greatly diminished (which can readily be 
done), that under no circumstances does the arc of so-called 
condensed light exceed or even equal in brilliancy the brightest 
part of the lurainous surface beyond. And this, which is found 
experimentally to be the case, can readily be shown to be neces- 
sarily so. In an article entitled * Notes on Brightness* in a 
weekly journal of science, I showed four years ago that by no 
optical contrivances can apparent brightness be increased, though 
quantity of light can of course be greatly increased. Venus in 
transit docs not differ in this respect from a portion of an enor- 
mous optical instrument ^directed towards the Sun, and the same 
general reasoning applies to her. It is, however, easily seen, if 
we take her case specially, that the law holds good. Thus, 
consider a small strip of the Sun*s disk lying on a diameter 
through Venus, — take two points along this strip separated by a 
distance ^r so small that the variation of the amount of refrac* 

LL 



460 Frofessor Zeriger^ Ah$orption of the TOUL 9, 

tion bj which rajs from points along the arc between these 
points reach the eye of a terrestrial observer may be considered 
uniform. Suppose that by the effects of refraction the distance 
cr, which seen directly from the Earth has that apparent length, 
is reduced in length, when forming a part of the arc of light 

round Venusy to j-^r^k being greater than unity. Then it is 

obvious that each pencil of rays from points along the luminous 
strip ^r has its divergency in the plane through the strip, Venus^s 
centre, and the Earth's, increased, as ^ : i, in passing along its 
course (whatever this may be) through the atmosphere of Venus. 
This follows from the uniform variation of the amount of 
bending for points differently placed along the strip hr. Hence 
the eye receives fewer rays from each point of the strip dr in the 
ratio of i : k. Wherefore, neglecting the absorptive effect of 
Ventis^s atmosphere, 

app. brlgbtness of strip $r seen round edge of $ : its app. brightness seen directly 

, . li ght reed, r onnd i from each pt. of strip ^ light reed, from each pt of strip directly 
apparent area of (trip as seen round ^ * apparent area of strip seen directly 

11^ I 



• • 






k* k ' «r 

i: I, 

or the brightness is unchanged. 

I may take this opportanity of noting that, in a paper op 
the Nebulee recently read before the Royal Society, it is asserted 
that an irresolvable stellar nebula would diminish in apparent 
brightness (so far as the stellar part of its light is concerned) with 
increase of distance. No reasoning is given in support of this 
assertion ; and I can see no reason for withdrawing the reasoning 
by which, in a paper on the Resolvability of Nebulee regarded 
as a Test of Distance, I show (incidentally) that a nebula so 
long as it 'remained irresolvable would be of constant intrinsic 
bri;f^htnes3 whatever its distance* (always supposing there is no 
extinction of light in traversing space). 

Margate, June 2, 1877. 



Absorption of the Light of Veniis hy Dark Violet Glass Plates, 

By Prof. Zenger. 

In October 1876 I observed Venus, to detect spots on it, and 
so look out for the alleged phosphorescent light of the dark part 
of the disk. I could observe Venus early in the morning during 
nearly the whole of Ootober ; it was then very brilliant, casting 
a shadow, and by its light making it possible to read the maps 
on the illuminated wall of the observatory. I could even see 

♦ I have since heard that Prof. Stokes, after the paper had been read before 
the Royal Society, indicated the error into which its writer had fallen in thia 
respect. 



Snpp. 1877. Light of Venus by Dark Violet Glaee Plates, 461 

the planet with the naked eye at 21^ 30"* and 2 1^40"* October 
II and 12, the atmosphere being very calm and pure. On 
September 30, 20^ i2°>, and the following day, October i, 
17^ i5°^» the disk was admirably defined in the telescope, and 
there was observed a very brilliant patch near the sonthem horn 
some two seconds or less from the terminator in the dark parts 
of the disk, and this was still visible for two days, when the 
terminator had passed it, shining like a brilliant star in the 
sarrounding part of the illnminated disk. 

This observation induced me to try a new method of photo- 
metric measurement by dark violet glass plates, putting one or 
two between the eye-piece and the eye, and determining the 
distance at which the light of a lamp vanished by one and then 
by two plates. I found the proportional intensity to be nearly 
I : 5'6 for one to two. Viewing the planet, it was very striking 
to observe the great diminution of light on the illuminated disk, 
as the borders vanished entirely by putting two plates before the 
eye. I lost sight of nearly one-third of the illuminated part, and 
the middle of it was with only one plate reduced to nearly one- 
third of its brilliancy. I therefore concluded that, putting the 
intensity of the most brilliant part of the planet =: i, and divid- 
ing the nearly one-half illuminated part in three parts, the in- 
tensities of each were nearly as 

1:1-5-3: 1 + 5*6, that is as 5-6 : 19 : i. 

It is obvious that, using a bi-prism with parallel planes, as for 
solar eye-pieces, and makmg one of the prisms of dark violet 
glass, the other being colourless crown glass, there will be a 
possibility of applying a scale of intensity by the difference of 
depth of the violet glass, and of measuring with more accuracy 
the intensity of such brilliant objects as Ventis, Jupiter, the Moon, 
&c. It seemed to me to be of interest to communicate these ob- 
servations, as they confirm the results by a quite different method 
published in one of the last Numbers of the Monthly Notices, and 
giving a new instance of very highly reflecting points on the sur- 
face of Venus (perhaps snow-covered high peaks) being visible, 
like on the Moon, before the solar light reaches the lower parts 
of the surrounding surface. I could never perceive any trace 
of the so-termed specular reflection, though I think it would 
have been perceived if there had been in the middle of the plane- 
tary disk such a higher intensity of reflected light in a round or 
elliptical shape. 

The diminution of light in the same longitude from the 
terminator seemed equal all over the disk of the planet, and not 
changed under different latitudes, as it should be in case of 
specular reflection. 

P.S. — Though I could detect a faint grayish light, sometimes 
ruddy near the terminator, during the time from September 30 
to October 14, the atmosphere bein'g uncommonly transparent, 
yet I could never see the whole of the dark part of Venw^ 

LL2 ^ 



463 Mr, H. 0. BusseUf Measures of a OerUaurt. Xxxvit. ^, 

thougli the planet afforded, from 16^ to 18^ in the morning of 
three days of October, a most splendid view. On the contraiy, 
it seemed with daybreak to be more easy to see the faint illumi- 
nation near the terminator, even to two-thirds of the whole 
breadth of the dark part of Venus. 
Prague^ Ftbruary 17, 1877. 



Measures of a Gentauri^ 1870 to 1877. 
By H. C. Russell, psq.. Director of the Sydney Observatory. 

As the double star a Gentauri did not arrive at periastron in 
1875 as predicted, perhaps the following measures of this in- 
teresting double, taken during the ordinary course of my obser- 
vatioiA on southern double stars, during the past seven years, 
may not be without interest. It is evident from these observa- 
tions that a' will not make its nearest approach to a' until about 
the end of this year. Its predicted arrival at that point was 
therefore nearly three years in error. It is my intention to 
observe it closely during the next few months ; and I hope to 
obtain such a series of measures as may serve to determine its 
periastron with accuracy. Some correction may be necessary to 
my position-angles, on account of personal bias, for I find that I 
do not measure the angle the same when the telescope is east as 
I do when it is west of the pier (see observations of July 20 and 
July 24, 1877), but I have not time to investigate the amount 
before this mail closes. 

The observations from 1870 to 1874 were made with a 7j-in. 
refractor by Merz, of 10 ft. 4 in. focus, and very fine defining 
power. The remainder have been made with an i i^-in. refractor 
by Schroeder, a very fine instrument. The method of observing 
is to place the position-wire bisecting both stars, and then make 
the distance wires bisect them. After reading, the position- wire 
is turned right away, and bronght back again, and the distance 
wires crossed ; each observation, therefore, which follows is an 
independent determination of the distance and position-angle. 
The only exception is the series September 27, 1870, when the 
lx)sition-circle was not moved after it was set the first time. 

All the observations, except those in 1870, were taken when 
the star was near the meridian. 

J^esults of Measures of DoubU Star a Ccntaurif at the Sk/dnet/ Observato-y. 

Bemarks. 

Definition pood; stars hare sharp 
round di.sks ; tolescopo 7| iQches ; 
P. 230 ; aperture 3 inches. 



Dnto. 
1870 

Sept. 27 


Position-Angle. 
/ 
21 5S 


Distono 

II 

100 






21 


58 


iro 






21 


58 


107 






21 


58 


107 




US 


21 


58 


96 


Men 


21 


58 


10*40 



Sopp. 1877. Mr. H. 0. BuuMf Meamrea of a Oenkmri. 463 



Dite. Pc 
1870 
Sept. 28 


•itioi] 



23 


i-Angle. 
24 


10-3 




24 


17 


10-3 




21 


44 


103 




21 


55 


II-O 


Means 


22 


50 


1047 


Oct 3 


22 


5 


lO-I 




22 


30 


iO'4 




22 


II 


103 




22 


16 


10*3 




22 


43 


10'2 


Means 


22 


21 


10-26 


Oct. 5 


21 


40 


IO-8 




21 


58 


iro 




22 


28 


10*3 




21 


44 


103 




22 


36 


III 


Means 


22 


5 


1070 


1871 
Jane 3 


23 


20 


io'6o 




21 


42 


10-31 




23 


13 


10-23 




23 


II 


10*27 




22 


13 


10-05 




23 


49 


10*46 




23 


8 


10-05 




22 


52 


10-03 




22 


33 


10*34 




23 


3 


io-i6 


Means 


22 


44 


10-25 


July 13 


22 


57 


10-05 




23 


15 


10*16 




22 


47 


9-86 




23 


23 


982 




23 


5 


10*21 


Means 


23 


5 


10-2 



Pjwi^y^Tff , 



Light donds about; stars very nn- 
steadj; telescope 7^; power 150. 



^ne clear night ; *' moonlight "; tele- 
scope 7^; power 150. 



Strong wind; much ribration; tele- 
scope 7i ; power 150. 



Power 230 ; telesi^pe 7 J. 



Stars dancing a good deal; tele- 
scope 7i. 



4<4 



Ur. Ei 0. Bimtia, Mtat»m9f a OeiOmmri, saWfi 



Silt*. Fodtioii-Aiigle. 
187a , 


Dlttuios^ 


June 7 26 13 


995 


as 43 


982 


26 3 


9-69 


as 40 


984 


as 5^ 


973 


as 48 


97S 


Heukf as 54 9*80 


July 5 as 


9-62 


24 46 


975 


a4 30 


9*62 


Kmiii 24 45 

• 


9*66 


1873 




Mij a 28 sa 


9-45 


28 45 


945 


27 S6 


9'66 


28 17 


9-66 


27 S9 


936 


28 37 


940 


Means 28 4 


950 


1874 




Jnne 13 30 16 


7-80 


30 26 


767 


29 33 


776 


29 21 


763 


30 19 


769 


30 13 


784 


' 30 6 


7-So 


30 3 


756 


30 21 


776 


29 29 


789 


Means 29 S9 


771 



Vei^ thick fog ; at timM BmoAf . 
ntible ; telasoope 7( ; power isa 



Stopped bj ekmds; meMiiM good; 
tefofoope n ; powm iy>. 



Stan dancing ; aperture of 3 inohes ; 
power 333 ; telescope 7^. 



Good definition;, measures good; 
power 140 ; telescope 7^. 



Supp. 1877. Mr. S. 0. BusieUf Measures of a OenUmri. 465 



Date. Foeitlon-Aiigle. 

1874 1 
June 29 30 19 


Dlgtance. 

II 
819 




30 


12 


817 




30 





793 




30 


8 


8-21 




30 


9 


8-08 




29 


53 


8-34 




30 


5 


8-45 




29 


44 


810 




29 


50 


8*47 




29 


58 


832 


Means 


30 


2 


823 


187s 


••• 


••• 


1876 








May 23 


45 


5 


4*39 




46 


30 


4-52 




46 





462 




46 


15 


4-55 




45 


40 


452 




46 


25 


4-57 




46 


35 


4-50 




45 


40 


452 




46 


10 


4-48 




46 


30 


427 


Moans 


46 


5 


449 


June 8 


47 


47 


42 




48 





3'8i 




47 


52 


430 




47 


10 


423 




48 


28 


470 




47 


42 


441 




48 


15 


438 




48 


10 


4*22 




48 


8 


420 




47 


10 


4*34 


Means 


47 


52 


4'20 



Benuurks. 



Good definition ; fall moon ; measures 
of distance not good; power 140; 
telescope 7^. 



Observer away in Europe. 



Stars tremnloos, and veiy watery; 
power 180 ; aperture 6 inches ; first 
measures with 11^ inches. 



Moderately steady; one disk seems 
about ^ more in diameter than the 
other; telescope 11^ ; power 544. 



4S6 



Mr. n. C. BtutM, U«an$nt ofaXkutamrL, xxstil 9^ 



Dsto. 


Foittloii^Aiigle. 


DisUuBoe. 


1877 





§ 


* 


Julys 


72 


56 


2713 




7a 


56 


2*803 




7* 


4« 


2*445 




73 


3 


2766 




72 


46 


2731 




72 


59 


2*481 




72 


31 


2*642 




73 


a4 . 


2*392 




72 


56 


2*427 




12 


36 


2*570 



Heanfl 72 52 



2*597 



July 7 



July 20 



72 


57 


ywf^n 


72 


31 


n 


78 


57 


1818 


79 


40 


2*179 


80 


25 


2*161 


80 


40 


1*999 


79 


33 


2179 


79 


15 


1-999 


78 


40 


2089 


78 


7 


2071 


79 


28 


2071 


79 


45 


2143 



Means 79 27 



2-071 



Aperinre 8 inehei ; power 450 ; ittZB 
dandzig; teUeoope ii|. 



6 me^Biires ; power 450. 

o (• •• oOO* 



11 



tt 



Telescope on wiest side of pier ; star 
2 hours before meridian ; definition 
not good ; aperture 5 inches; power 
500; telescope ii|. 



Jnly 24 



75 


40 


2-269 


76 


30 


2-071 


75 


55 


2*125 


75 


35 


2*071 


76 


12 


2-287 


75 


45 


2*105 



Aperture 7 inches; power used 800; 
telescope on east side ; star 2 hours 
past meridian ; telescope 11^ inches. 



Means 75 56 



2*155 



Sopp. 1877. Bev, S, J. JohnsoUf Observations on Lunar Eclipse. 467 



Dftte. Fo 


Bition- 


-Aoglfi. 


Distance. 


1877 





# 


// 


July 2$ 


76 


50 


2089 




75 





2197 




77 


35 


2089 




77 


3 


2197 




76 


28 


2'l6l 




76 


5 


1-927 




76 


20 


1999 




75 


20 


2053 




77 


40 


2*215 




77 


30 


2143 




76 


30 


2- 1 79 




75 


15 


2017 




76 


10 


2251 




75 


30 


2071 


Means 


76 


22 


2113 


Sydney Observatory^ 
July 27. 1877. 





BemarkB. 

Aperture 5 inches ; powet 800 ; tele- 
scope on east side of pier; defi- 
nition not very good ; stars dancing. 
Great care taken witii these obser- 
vations, but the position-angle is 
very difficult, owing to the motion 
or unsteadiness of the stars. Clouds 
were passing, and at times obscured 
both stars, but oftener only a', 
which I estimate as folly one-third, 
or nearly one-half, less than a}. 
The varying thickness of the clouds 
enabled me to estimate the relative 
brilliance. 



Observations of the Lunar Eclipse, 1877, August 23. By tho 

Bev. Samuel J. Johnson. 

The total eclipse of the Moon was seen here as well nnder an 
English as nnder an oriental sky, not a cloud intervening through- 
out. I employed a power of 70 on 2 J in. 

9.10 Penumbra dimmed theN.E. quadrant of the Moon con- 
siderably. At 8.45 I had not been able to satisfy 
myself about the presence of it. Precise time of 
conmiencement diffictdt to determine. At 9.15 the 
shadow was evidently impinging on the neighbour, 
hood where Olbers is marked. 

9.18^ Immersion of Orimaldi, 

9.22^ Shadow reached Aristarchus, 

9.32I Copernicus reached. For 3 min. or 4 min. an orange 
tint has been visible at the edge of the Moon. Aris" 
tarchus comes out most distinctly in the shadow. 

9-391 PlcLto reached. 

9.40^ Archimedes reached. 

9.49^ Tycho reached. Aristoteles same time. Copper tint 
readily seen with unassisted vision. 

9.51 Immersion of Tycho. 



468 Bev, S. J. Johnson^ Lwnar Eclipse, 1877, Aug. 23. xxrm. 9, 

9.55 The three i^'s mA^aritu coming into view to the naked 
eye. 

10.5 So-called seas in the eclipsed Moon beginning to be 
very prominent. Mare SerenitcUis standmg out nearly 
black, darker than any other part of the lunar 
sar£EU3e. 

10. 13 J Immersion of Mare Grisium. Mare Orisium, Mare 
FoecunditatiSj and the region sonth of them of a 
greenish hue. The rest of the eclipsed disk of a 
coppery tint. 

io.i8'2 Emersion of a star about mag. 7^ &om a point in a 
line with south extremity of Mare Grisium. Angle 
abortt 100®. 

10.20 Total obscurity. 

10.24*9 Star mag. 7 occulted, angle about 8o^ It exhibited the 
illusion of projection more plainly than I have ever 
noticed, appearing to lie within the Moon's limb 
3' or 4'. 

ii.8'o Emersion of small star mag. 8. Angle about iio^ 

1 1 . 1 5 The central regions darkest, being about the time of mid- 
eclipse ; the illumination round the borders tolerably 
* uniform now. 

1 1.45 Crescent of yellow light on Moon's eastern limb. Mare 
Grisium, Fcecunditatis, Nectaris, Tranquilitatis, Sereni' 
talis in a smoky gloom ; above and below this region 
the prevailing tint orange. 

12.4^^ First streak of sunlight. This outbreak was so clearly 
marked that it might have been noticed by the 
naked eye within 3* or 4' of the instant the telescope 
showed it. 

1 2. 7 J Emersion of Grimaldi. 

12.14^ Emersion of Aristarcli 11s, 

12.27^ Emersion of Copemicws. 

12.30^ Emersion of Plato. 

12.31^ Emersion of Tycho. 

12.35 Emersion of Archimedes. Milky Way beginning to fade 
out of sight, now half the Moon is uncovered. 
A slight brownish tinge mingling with the grey could be 
detected until 12.55. 

1 3.0 J Mare Grisium began to emerge. 

13.5 Emersion of the Mare Grisium. 

A few degrees north of this, the shadow left the Moon 
about 13.8^. 

(Angles of Stars occulted reckoned same way as in N,A.) 



Sapp. 1877. On Spectnim of WitinecJce^a Comet etc. 469 

There was an absence of that flickering light on the reddened 
disk of the Moon which I noticed last February, and which was 
probably dae simply to the nndnlations of oar own atmosphere, 
bnt which Professor Doma of Turin ascribed to the action of 
a lunar aurora, saying that the refraction of the Sun's rays 
within the cone of the Earth's shadow was not an adequate 
explanation. (See L^ Opinions NaaionaXe^ March 3). 

I had requested another observer, only 35 sec. long, further 
east than here, to note the time of the first outbreak 01 sunlight 
on the Moon, as a simultaneous observation, and the result gave 
a difference of longitude almost precisely accurate. 

Ufton Helion$ Eeciory, Crediton, 



On the Spedrtmi ofConiet 6 1877 (Wtnneche^s) and of the Eclipsed 
Moon, observed at the Boyal Observatory, Greenwich. 

{Communicated hy the Astronomer SoyaL) * 

The position of Comet b 1877 was so inconvenient for ob- 
servation with the Great Equatoreal when armed with the long 
Single Prism Spectroscope, that it was found practically im- 
possible to obtain any measures of the bands in the Spectrum, 
though on May 15 the Dun Echt Observations (Monthly Notices, 
1877, June) were so far confirmed that the spectrum of the coma 
was found to consist of three bands in the neighbourhood of the 
three principal carbon bands, wave-lengths 4834, 5203, and 
5607, whilst that from the nucleus appeared to be contmuous. 
For more exact determination of position, a small Half Prism 
Spectroscope, giving a dispersion of 20° from A to H with a 
magnifying power of 9 on the viewing telescope, was used, and 
this, being only 16 inches in length and consequently much 
shorter than the other spectroscope, allowed sufficient room for 
the observer within the polar axis. With this greater dispersion 
the spectrum of the nucleus no longer appeared continuous, and 
the wave-length of the brightest band was determined (by six 
indirect comparisons with the carbon band 5203) to be 5178, 
with a probable error of 5 toDth-metres. The measures were 
made by turning the half-prism by means of a screw, so as to 
bring the cometary band to coincide with the bright reference 
hne formed by the image of the comet on the slit, and then 
comparing the latter with the band in the carbon spectrum. 

During the Eclipse of the Moon on 1877 August 23, the 
spectrum was observed with the Single Prism Spectroscope 
during totality and also during the partial phase, when the 
portion of the Moon's disk still in the umbra was repeatedly 
compared with the part which had emerged. During totality 
(about 11^ O.M.T.) a strong absorption band was seen in 
the yellow, and the red and blue ends of the spectrum were 



470 On Spectrum of Wvnneeke^s Comet etc, xixvu. 9. 

completely cnt off, whilst the orange was greatly redaced in 
intensity. The yellow and green were comparatiyely bright, and 
in fact appeared at a first glance to constitute the whole visible 
spectrnm. The wave-length of the more re&angible edge of the 
strong absorption band was found, from a mean of 9 measures, to 
be 5624 + 5, and at about 11^ it extended to wave-long^h 5900, 
i.e. as far as D. As the end of the total phase approached 
(12^ 4™), the band became narrower, its bi^adth bein^ only 
twice the interval of the D lines at 11^ 45™, and at 12" 20™, 
daring the partial phase, it was reduced to a mere line on the 
eclipsed portion. This band is coincident with the strong 
band c of the atmospheric spectrum as given by Brewster and 
Gladstone, which is peculiarly characteristio of the spectrum 
of light which has passed through a thick stratum of air. The 
red end of the spectrum was cut off by a dark band commencing 
about halfway from D to C, in which a black line was suspected. 
About the middle of totality a dark band, commencmg at 
5080 + (near band c of the Brewster-Gladstone spectrum) cut 
off all the rest of the spectrum, but later on at 11^ 30™ the 
spectrum was visible as &r as about 4930 (the position of baud k 
in the atmospheric spectrum). After the end of totality the red 
and blue ends of the spectrum from the eclipsed portion became 
visible beyond these limits. The appearance of the spectrum of 
the part clear of the umbra, though still in the penumbra, was 
totally different, even when reduced to the same degree of 
faintness by closing the slit. In this case the spectrum faded 
out as a whole from beyond D to near G in the violet. 

The part of the Moon examined when the band c was darkest 
was the region of Mare Nectaris and Mare Fcecunditatis, and the 
band could be seen only on the darkest part of the Moon when 
Kepler was just emerging from the umbra, growing rapidly 
fainter as the spectroscope was moved away towards the bright 
part. 

The light by which the eclipsed Moon is visible would thus 
appear to have passed through a great thickness of the earth's 
atmosphere, givmg rise to the peculiar copper colour. 

The observations were made by Mr. Christie and Mr. 
Maunder. 

Boyal Observatory f Greenwich^ 
1877, August 28. 




INDEX. 



PAOl 

Abbb, on 0. M. Mitchers observations at Cincinnati 121 

Abney, Capt. W. de W., effect of a star's rotation on its spectrum 278 

Airj, Sir G. 6., note on his numerical lunar theory 245 

• — Oral address on suspected intra-mercurial planet, and on 

approaching opposition of Mars 246 

See Greenwich Ol^ervatory. 
Altazimuth stand, on a method of obtaining equatoreal motion by a 

simple addition to, Lord Lindsay I 

- — ' description of an improved, for reflecting telescopes, 

with a new form of binocular eye-piece, Mr. Thorn thwaite 3 

Andr^, M. Ch., on his diffraction experiments, and observations of 

transits, Mr. Perry 56, 59 

Angot,'A., ^tude sur les images photographiques obtenues au foyer des 

lunettes astronomiques 387 

■ sur Tapplication dela photographie a Tobservation du passage 

de Venus 392 

Arcimis, Seiior, observations' of the Lunar Eclipse of 1876, September 3, 

made at Cadiz 12 

on the visibility of the unilluminated portion of the disk 

of Venus 259 

— phenomena of Jupiter* s satellites, observed at Cadiz tS. 

observations of occultations of stars by thd Moon, made 

at Cadiz in the year 1876 261 

— ^ Lunar Eclipse of the 27th February 1877, observed 

at Cadiz 400 

Ariadne^ on the opposition of the minor planet, as a means of determining 

the solar parallax, Mr. Gill 327 

Astronomy, report on the progress of, in the year 1876-77 : — 

The numerical lunar theory 180 

Reduction of the observations of the transit of Veniis^ December 8, 

1874 181 

M. Le Verrier's planetary researches 184 

The Nautical Almanac for 1880 185 

Solar physics %b. 

Discovery of minor planets 188 

Discovery of a new comet 189 

D'Arrest's periodical comet ib, 

Santiago de Chile observations 190 

Physical observations of Saturn 191 

Observations of Jupiter's satellites at Adelaide 1 92 

Drawings oi Jupiter 0), 

The supposed discovery of the object perturbing the motion of 

Procyon 193 

Photographs of spectra of stars 195 

New double stars ib. 

Micrometric measures of double stars 196 

Doberck's new elements of the orbit « Leonis 197 

Dun Echt Observatory publications 199 

The new star in Ougnus 200 

Suspected change in nebula Messier, No. 17 (the Horseshoe nebula) 202 

Montigny's researches on scintillation 203 

Progress of meteoric astronomy in the year 1876 205 

— ^-— __ correction 36a 



472 Index, 

PAOK 

Backhouse, J. W., on the nomenclature of meteor radiant points 281 

Ball, Prof. R. S., obserTations of minor planets with the transit^circle at 

Dublin (Dunsink) 14 

. ..^....^^^ note on a transformation of Lagrange's equations of 

motion in generalised co-ordinates, which is conrenient in 

physical astronomy 265 

Boe, H. de, on a method of destroying the vibrations on a meiturial 

reflector 409 

Brett, J., the specular reflexion hypothesis, and its bearing on the transit 

of Venu$ 126 

Brightness, apparent, as an indication of distance in stellar masses, Mr. 

Stone 232 

Bumham, S. W., note on the double star 9 ^* ^^ 280 

Campbell, Capt. W. M., on a peculiarity of personal equation 283 

Capron, J. K, report of Examination of Sun*s disk. at Ouildford, March 

21, 22, and 23, for suspected planet Vulcan 348 

Cayley, Prof. A., on spheroidal trigonometry 92 

— — ^— addition to Prof. Ball's paper on Lagrange's equations 

of motion 269 

Christie, W. H. M., on the effect of wear in the micrometer-screws of the 

Greenwich transit-circle 18 

—— . note on the gradation of light on the disk of Venus 90 

Comets: 

1877. L Borelly 189,360 

„ IL Winnecke 359, 360 

D' Arrest's (search for) 360 

." 6 and c, 1877, Spectra of, Lord Lindsay 430 

6, 1877, spectrum of 469 

Copeland, Dr. K., on two "flats" in the Moon's limb, observed March 

23. 1877 432 

Darwin, G. H., on an oversight in the M^canique Celeste, and on the 

internal densities of the planets 77 

Denning, W. F., obs(?rvations of shooting stars, April to December 1876 105 

— -. radiant points of shooting stars, from Capt. Tupman's 

unreduced observations, 1869-71 349 

Diffraction experiments, on those of M. C. Andre with reference to astro- 
nomicul instruments, and the general theory of this diffraction, 

Mr. Perry 56 

Downing, A. W., a deterraination of the semi-diameter of Venus at the 

mean distance of the Sun from the Earth 398 

correction to foregoing paper 442 

Dreyer, J. L. E., note on some of M. Stephan's now nebula 427 

Dun Echt Observatory Publications 232 

Eclipses: 

lunar of 1876, September 3, S. Arcimis 12 

1877, February 27, Mr. Penrose 262 

»> » ,> Mr. Perry 263 

„ „ „ S. Arcimis 400 

„ August 23, Mr. Johnson 467 

,, ,, ,, spectrum observations 469 

Eclipse, solar of 1876, September 17, Mr. Tebbutt 1 1 

EUery, R. L. J., observations on a Centauri 435 

Equinoctial time, table for facilitating the determination of, Admiral 

Shadwell 401 

Erck, W., an improved mode of viewing the Sun 128 

Errata 282 

Eye-piece, a new solar, Prof. Zenger 439 



Index. 473 

PAOB 

FellowB deceased, list of 143 

Sheepshanks, Miss Ann (Honorary) i6. 

Becker, Bear-Admiral A. S 145 

Cheyne, C. H. H 147 

Corbet, Lieut. C, R.N 148 

Edwards, the Rev. J 150 

Middlemist, the Rev. R 151 

Otter, Rear-Admiral H. C 152 

Rosaz, the Cheyalier F. de ••• 153 

Strange, LieQt.-Col. A, 154 

Yeates, A. -. 159 

Fellows elected i, 41, 93, 129, 231, 283,.363, 427 

Fiiilay, W. H., a method of deducing the formula for correcting the 
computed time of an observed occultation for errors in the 

elements adopted 16 

Qasparis, H. A. de., on Kepler*s problem 263 

Oill, D., on the proposed expedition to observe the approaching opposition 

of Mars 310 

— — on the opposition of the minor planet Ariadne as a means of 

determining the solar parallax 327 

— ~ on the opposition of the minor planet Melpomene, as a means of 

determining the solar parallax 412 

Glaisher, J. W. L., on an elliptic function solution of Kepler's problem 366 

, on the solution of Kepler's problem 445 

Gledhill, J. W., and Wilson, J. M., a preliminary list of binary and other 

interesting double stars 64 

Green, N. £., note on the coming. opposition of Mars 424 

Greenwich Observatory. Spectroscopic results for the motions of stars, 

and of Venus in the line of sight, and for tlie Sun and Jupiter 22 
^— — ^— spectroscopic results for the rotation of Jupiter, 

and of the Sun 43 

observations of occultations of stars by the Moon, 



and of phenomena of Jupiter^s satellites, made in the year 

1876 116 

— stars to be compared in R.A. with Mars 1877, 



for determination of the parallax of il/ar^ 117 

on spectrum of Comet h 1877 (Winnecke's) and 



of the eclipsed Moon, August 23 469 

Harkness, Prof., W., theory of the horizontal photoheliograph, including 
its application to the determination of the solar parallax by 

means of transits of TefiMJ. (Abstract.) 93 

Hind, J. R., on the orbit of a Ceniauri 96 

— — . on two ancient occultations of planets by the Moon, 

' observed by the Chinese 243 

Holden, Prof. R S., The nebula in Orion, request to Astronomers 231 

Hewlett, Rev. F., his Sun-spot drawings 364 

Johnson memorial prize 362 

Johnson, Rev. S. J., visible transits of Mercury to the year 2CXX) 425 

— — ^— lunar eclipse of 1877, August 23 467 

Juno, note on the results of heliometer observations of, to determine its 

diurnal parallax. Lord Lindsay and Mr. Gill 308 

Jupiter, ephemeris for physical observations of, Mr. Marth 24 1 

— , spectroscopic observations for rotation of 22, 43 

Jupiter* s satellites, phenomena of, observed at the Greenwich Observatory 116 

-^.^ — at Cadiz, Senor Arcimis 259 

at the Observatory, Adelaide, and 

notes on the physical appearance of the planet, Mr. Todd 284 

«...i.....«,«.........«ii-«.-...— —...—i— at the Radcliffe Observatory, Oxford 340 




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